Method and alarming system for CO2 sequestration

ABSTRACT

Methods and an alarming system for long-term carbon dioxide sequestration in a geologic reservoir are described. The geologic reservoir may be a water filled sandstone reservoir or a carbonate reservoir. A reservoir model is constructed to show the effects of varying injection pressures, the number of injection wells, the arrangement of injection wells, the boundary conditions and sizes of the reservoir on caprock uplift, fracture formation and fracture reactivation. The alarming system generates an alarm when caprock uplift that surpasses a threshold is detected. The injection pressures and the number of injection wells operating may be varied in response to the alarm.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to Provisional Application No.62/813,473 entitled “A Technique To Relate The Fracture Dimensions AndLocation In The Caprock With The Ground Uplift” filed on Mar. 4, 2019,the entire contents of which is incorporated herein in its entirety.

STATEMENT OF ACKNOWLEDGEMENT

The inventors would like to acknowledge the support of the Science &Technology Unit at King Fand University of Petroleum & Minerals (KFUPM),Award No. TIC-CCS-1 through the National Plan for Science, Technologyand Innovation (MAARIFAH) - King Abdul-Aziz City for Science andTechnology (KACST).

BACKGROUND Technical Field

The present disclosure is directed to methods and an alarming system forcarbon dioxide sequestration.

Description of Related Art

The “background” description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description which may nototherwise qualify as prior art at the time of filing, are neitherexpressly or impliedly admitted as prior art against the presentinvention.

Global climate change has been of concern due to global temperatureincreases during the last few decades. One of the major causes of globalwarming is believed to be the excessive emission and accumulation ofgreenhouse gases in the atmosphere, especially carbon dioxide. TheUnited Nations Intergovernmental Panel on Climate Change (IPCC) hastracked climate change since 1988. The IPCC 2005 report, which wasprepared by 100 authors and reviewed by 200 experts from all over theworld, stated that the potential of carbon dioxide storage capacity ingeological formations is at least 2000 gigatons. Geological reservoirsare able to retain 99% of stored carbon dioxide over the first 100 yearsof the loading period, before the onset of leakage from the reservoir.(See Bert M et al., “IPCC special report on carbon dioxide capture andstorage”. 2005, Cambridge University Press, United States of America,incorporated herein by reference in its entirety).

An IPCC 2014 report suggested increasing research related to thegeological storage of carbon dioxide, in order to slow down globalwarming. (See IPCC (2014) Climate Change 2014. “Observed changes andtheir causes”. Intergovernmental panel on climate change, incorporatedherein by reference in its entirety).

It has been proposed to capture the excess amount of CO₂ in theatmosphere and permanently store it in underground sedimentaryreservoirs to mitigate the effect of global warming. (See Bruant R G Jet al (2002) “Safe storage of CO₂ in deep saline aquifers”.Environmental Science & Technology 36:240-245; Sams W, Grant B, SinishaJ, Turgay E, Duane HS (2005) “Field-Project Designs for Carbon DioxideSequestration and Enhanced Coal bed Methane Production”. Energy & Fuels19:2287-2297; Torvanger A K, Rypdal S (2005) “Geological CO₂ storage asa climate change mitigation option”. Mitigation and AdaptationStrategies for Global Change 10(4):693-715; and Xiping W, Hongdou Z(2018) “Valuation of CCS investment in China's coal-fired power plantsbased on a compound real options model”. Greenhouse gases-science andtechnology 10.1002/ghg.1809, 1-11, each incorporated herein by referencein their entirety).

One way to reduce global warming is to remove the already releasedcarbon dioxide from the environment by introducing some external speciessuch as liquid droplets and other particulate matters in theenvironment. The liquid droplets and the particulate maters will capturethe gas and remove it by gravity. (See Shukla, J. B., Chauhan, M. S.,Sundar, S. and Naresh, R. (2015) “Removal of carbon dioxide from theatmosphere to reduce global warming: a modelling study”, InternationalJournal of Global Warming, Vol. 7, No. 2, pp. 270-292b, incorporatedherein by reference in its entirety).

Data centers have been cited as a cause of about 2% of global warming.The main sources of greenhouse gas emission in data centers are theservers used for data processing. (See Uddin, M., Memon, J., Rozan, M.Z. A., Alsaqour, R. and Rehman, A. (2015) “Virtualised load managementalgorithm to reduce CO₂ emissions in the data center industry”,International Journal of Global Warming, Vol. 7, No. 1, pp. 3-20,incorporated herein by reference in its entirety).

Carbon dioxide has been captured from major emission sites, such as datacenters, and stored in deep underground reservoirs. This capture andstorage of carbon dioxide in geological reservoirs was introduced in the1970s. Carbon capture and storage (CCS) has been focused on sources ofCO₂ such as power plants, data centers and industrial processes. Theprocess of carbon capture and storage (CCS) has been shown to becommercially viable and has been developed in many countries. (SeeShukla R, Ranjith P, Choi S, Haque A (2011) “Study of Caprock integrityin geo-sequestration of carbon dioxide”. Int J Geomech:294-301.https://doi.org/10.1061/(ASCE)GM.1943-5622.0000015, incorporated hereinby reference in its entirety).

During the process of carbon capture and storage (CCS), carbon dioxideis captured from large point sources of carbon dioxide like power plantsand industries and then transported to a storage location, where it isstored in deep underground geological reservoirs. CO₂ can be stored indepleted oil reservoirs, deep saline aquifers, or deep coal seams. (SeeCristina, R., Maria, A. D. and Manuel, J. L. (2013) “Unconventional coalreservoir for CO₂ safe geological sequestration”, International Journalof Global Warming, Vol. 5, No. 1, pp. 46-66; and Sally, M. B. and David,R. C. (2008) “Sequestration in deep sedimentary formations”, Elements,Vol. 4, No. 1, pp. 325-331, each incorporated herein by reference intheir entirety). The option of geological storage of CO₂ was proposedfor the first time in the 1970s. Carbon dioxide was stored for the firsttime in Sleipner gas field in the North Sea in 1996. (See Torp, T.A. andGale, J. (2003) “Demonstrating storage of CO₂ in geological reservoirs:the Sleipner and SACS projects”, in Amsterdam 2003: Proceedings of the6th International Conference on Greenhouse Gas Control Technologies,Pergamon, Amsterdam, pp. 311-316, incorporated herein by reference inits entirety).

During the process of carbon dioxide sequestration, CO₂ is injected at ahigh injection pressure which is greater than the reservoir porepressure into a reservoir deep below the ground level. For efficient CO₂sequestration, the reservoir should be at a depth greater than 800meters, with high porosity for storing the incoming CO₂ and highpermeability to ensure the CO₂ mobility in the reservoir even at lowinjection pressures. (See Anders, H. and Marten, B. (2009) “Expertopinions on carbon dioxide capture and storage—a framing ofuncertainties and possibilities”, Energy Policy, Vol. 7, No. 6, pp.2273-2282, incorporated herein by reference in its entirety). At a depthmore than 800 meters, CO₂ is in a denser form which increases thestorage capacity as it has less volume. Moreover, the injection intodeeper reservoirs minimizes leakage of CO₂ into ground water. Theobjective of the CCS process is to store a maximum amount of CO₂ in areservoir without sacrificing the integrity of the reservoir, the underburden and over burden layers, and the environment above the groundlevel. (See Gibbins, J. and Chalmers, H. (2008) “Carbon capture andstorage”, Energy Policy, Vol. 36, No. 12, pp. 4317-4322; and Mark, D. Z.and Steven, M. G. (2012) “Earthquake triggering and large-scale geologicstorage of carbon dioxide”, National Academy of Sciences USA, Vol. 109,No. 26, pp. 10164-10168, each incorporated herein by reference in theirentirety). Considering the maximum possible occupancy of the varioustypes of sedimentary reservoirs, the depleted oil and gas reservoirshave a CO₂ storage capacity between 675 and 900 billion tons, whileunmineable coal can store between 3 and 200 billion tons, and salineaquifers have a capacity between 1,000 and 10,000 billion tons. (SeeSally and David, 2008). The CO₂ storage capacity estimation for areservoir is mainly based on various factors like the available porosityof the reservoir, the reservoir pressure, and estimates of the changesin the density and volume of CO₂ at the reservoir pressure. At greaterdepths, the density of carbon dioxide increases and the volumedecreases. (See Bachu, S. et al. (2007) “CO₂ storage capacityestimation: issues and development of standards”, International Journalof Greenhouse Gas Control, Vol. 1, No. 1, pp. 62-68, incorporated hereinby reference in its entirety).

Before injecting carbon dioxide, it must be confirmed that the reservoiris capped with impermeable caprock and that the reservoir has highpermeability for the flow of the injected carbon dioxide. Depleted oiland gas reservoirs, coal seams, and saline aquifers are desirable sitesfor storing carbon dioxide for sufficiently longer periods of time. (SeeAshkan B et al (2013) “Simulation study of CO₂ sequestration potentialof the Mary Lee coal zone, Black Warrior basin”. Environmental EarthSciences 70:2501-2509; Cristina R, Maria A D, Manuel J L (2013)“Unconventional coal reservoir for CO₂ safe geological sequestration”.International Journal of Global Warming 5(1):46-66; and Sung SP et al(2016) “Numerical modeling of the tensile fracture reactivation underthe effects of rock geo-mechanical properties and heterogeneity duringCO₂ storage”. Environmental Earth Sciences, 75: 298-303, eachincorporated herein by reference in their entirety).

Carbon dioxide injected into a sedimentary reservoir is adsorbed in thereservoir matrix grains. The adsorption of carbon dioxide in thereservoir causes deformation, which subsequently reduces thepermeability of the porous medium. As the permeability of the reservoiris reduced the mobility of carbon dioxide is reduced in the reservoirand hence the reservoir becomes less receptive to storing more of theincoming carbon dioxide at the same injection rate. (See Perera, M. S.A. et al. (2011) “A review of coal properties pertinent to carbondioxide sequestration in coal seams: with special reference to Victorianbrown coals”, Environmental Earth Sciences, Vol. 64, No. 1, pp. 223-235;and White, C. M., Smith, D. H., Jones, K. L., Goodman, A. L., Jikich, S.A., Lacount, R. B., Dubose, S. B., Ozdemir, E., Morsi, B. I. andSchroeder, K. T. (2005) “Sequestration of carbon dioxide in coal withenhanced coal bed methane recovery: a review”, Energy & Fuels, Vol. 19,No. 3, pp. 659-724, each incorporated herein by reference in theirentirety).

Among sedimentary reservoirs, the naturally fractured reservoirs, suchas carbonate depleted oil and gas reservoirs, can store large amounts ofcarbon dioxide due to their highly porous structure. (See Stevens, S.H., Kuskraa, V. A., Gale, J. J. and Beecy, D. (2000) “CO₂ injection andsequestration in depleted oil and gas fields and deep coal seams:worldwide potential and costs”, AAPG Bulletin, Vol. 84, pp. 1497-1498,incorporated herein by reference in its entirety). Depleted oilreservoirs and gas reservoirs are normally at depths greater than 800meters, which implies that CO₂ will be stored in its supercritical form.(See Al-Shuhail, A.A., Al-Shuhail, A.A. and Khulief, Y.A . (2014) “CO₂Leakage Detection using Geophysical Methods under Arid Near-surfaceConditions”, Progress Report of KACST TIC-CCS Project number TIC-CCS-1;and Qu, H. Y., Liu, J. S., Pan, Z. J. and Connell, L. (2010) “Impact ofthermal processes on CO₂ injectivity into a coal seam”, TOP ConferenceSeries: Materials Science and Engineering, Vol. 10, pp. 1-10, eachincorporated herein by reference in their entirety).

Further, CO₂ in its supercritical form causes greater swelling of thereservoir matrix than when in the sub-critical form, which may causesignificant reduction in reservoir permeability. (See Kiyama, T. et al.(2011) “Coal swelling strain and permeability change with injectingliquid/supercritical CO₂ and N₂ at stress-constrained conditions”,International Journal of Coal Geology, Vol. 85, No. 1, pp. 56-64; andPerera et al., 2011, each incorporated herein by reference in theirentirety).

Although the maximum occupancy of a sedimentary reservoir can becalculated from the porous volume and the volume and density of CO₂ atthe reservoir pressure, the reduction in permeability is due to theadsorption induced strain restricting the transport of CO₂ beyond acertain region around the injection well. (See Kiyama et al., 2011; andWu, Y., Liu, J. and Elsworth, D. (2010) “Dual poroelastic response of acoal seam to CO₂ injection”, Int. J. Green H. Gas Control, Vol. 4, No.4, pp. 668-6′78, each incorporated herein by reference in theirentirety). Increasing CO₂ injection pressure can increase the mobilityof CO₂ to a certain limit, which is bounded by the maximum safe value ofthe injection pressure for reservoir stability.

The most practical way to transport CO₂ to all portions of the reservoirand to store the maximum safe volume of CO₂ is to utilize multipleinjection wells. The optimum number and arrangement of the injectionwells is unique for a given reservoir based on its size and geologicaldescription. (See Rutqvist, J., Vasco, D. W. and Myer L. (2010) “Coupledreservoir-geo-mechanical analysis of CO₂ injection and grounddeformations in In Salah, Algeria”, Int. J. Greenh. Gas Control, Vol. 4,No. 2, pp. 225-230; and Zhang, H. B., Liu, J. and Elsworth, D. (2008)“How sorption-induced matrix deformation affects gas flow in coal seams:a new FE model”, Int. J. Rock Mech. Mining Sci., Vol. 45, No. 8, pp.1226-1236, each incorporated herein by reference in their entirety).

Carbon dioxide storage projects at San Juan, Sardinia, and Ishikaribasins, show a reduction in reservoir permeability due the adsorptioninduced strain; thus attesting to the significance of the role ofmultiple injection wells in attaining the maximum storage capacity. (SeeReeves, S. (2001) “Geological sequestration of CO₂ in deep, unmineablecoal beds: an integrated research and commercial-scale fielddemonstration project”, SPE 71749: Presented at SPE Annual TechnicalConference and Exhibition, New Orleans, Louisiana; Amorino, C. (2005)“CO₂ geological storage by ECBM techniques in the Sulcis area (SWSardinia Region, Italy)”, Paper presented at Second InternationalConference on Clean Coal Technologies for our Future, Sardinia, Italy;and Botnen, L. S. et al. (2009) “Field test of CO₂ injection and storagein lignite coal seam in North Dakota”, Energy Procedia, Vol. 1, pp.2013-2019, each incorporated herein by reference in their entirety).

Modelling tools which have been utilized for the coupled carbon dioxideflow and reservoir deformation analyses for both single porosity andnaturally fractured reservoirs are COMSOL, CMG, COMET3, TOUGH2 andECLIPS. (See COMSOL [Computer software]. COMSOL Inc., Burlington, Mass.;CMG-GEM [Computer software]. Computer Modelling Group, Calgary, Alberta,Canada; Godec M, Koperna G, Petrusak R, Oudinot A (2013) “Assessment ofFactors Influencing CO2 Storage Capacity and Injectivity in EasternU.S”. Gas Shale Energy Proceeding 37:6644-6655; Guo C, Wei M, Chen H,Xiaoming H, Bai B (2014) “Improved Numerical Simulation for Shale GasReservoirs”. Proc., Offshore Technology Conf.-Asia, OTC-24913, OffshoreTechnology Conference, Kuala Lumpur, Malaysia, 1-17; Pruess K,Nordbotten J (2011) “Numerical simulation studies of the long-termevolution of a CO₂ plume in a saline aquifer with a sloping caprock”.Transport in Porous Media 90(1):135-151; Wang et al (2016) “Impacts ofstratum dip angle on CO₂ geological storage amount and security”.Greenhouse gases-science and technology 6(1):682-694; Amirlatifi, A.(2013) “Coupled Geomechanical Reservoir Simulation”, Dissertation,Missouri University of Science and Technology, Print; Rutqvist et al.,2010; and Tran, D., Buchanan, W. L. and Nghiem, L. X. (2010) “Improvedgridding technique for coupling geomechanics to reservoir flow”, SPEJournal, Vol. 15, No. 1, pp. 64-75, each incorporated herein byreference in their entirety).

COMSOL allows conventional physics-based user interfaces and coupledsystems of partial differential equations for modeling the flow ofcarbon dioxide in the reservoir and the corresponding deformation of thereservoir. COMSOL multiphysics software can be used to performequation-based modeling in which a set of equations determine the gasflow and reservoir deformation. For modeling the geo-mechanical behaviorof a reservoir undergoing carbon dioxide injection, a representativemodel of the reservoir is needed. Suitable boundary conditions areneeded to solve the carbon dioxide flow and reservoir deformationequations. During the geo-mechanical modeling of the reservoir,different types of boundary conditions must be applied to the simulationmodels.

Conventionally, separate simulators have been used for flow of carbondioxide and reservoir geo-mechanical analysis. Using separate toolscreates new challenges for simulator interfacing because the output fromthe flow simulator is used in the deformation simulator and similarlythe output of deformation simulator is used in the flow simulator foreach time interval. Using two simulators also increases the processingtime. The equation-based modelling option in COMSOL multiphysics solvesthe above mentioned problems and also has the capability of using newermathematical models for flow and geo-mechanical analysis of naturallyfractured reservoirs. (See Holzbecher, E. (2013) “Poroelasticitybenchmarking for FEM on analytical solutions”, Excerpt from theProceedings of the COMSOL Conference, Rotterdam, pp. 1-7; Tore, B.,Eyvind, A. and Elin, S. (2009) “Safe storage parameters during CO₂injection using coupled reservoir geo-mechanical analysis”, Excerpt fromthe Proceedings of the COMSOL Conference, Milan, pp. 1-7; COMSOLMultiphysics (1998-2016) “Introduction to COMSOL Multiphysics”, pp.1-194,https://cdn.comsol.com/documentation/5.2.1.262/IntroductionToCOMSOLMultiphysics.pdf;and Bogdanov, El Ganaoui, K. and Kamp, A. M. (2007) “COMSOL 2Dsimulation of heavy oil recovery by steam assisted gravity drainage”, inProceedings of the European COMSOL Conference, each incorporated hereinby reference in their entirety).

Before starting the injection process, a feasibility study of the targetreservoir by means of geo-mechanical modeling has been recommended toprovide for the safety of the reservoir during carbon dioxide injection.Safe storage means that buoyant carbon dioxide and associated gases,collectively referred to as gaseous emissions injected into a fluidfilled subterranean formation will not leak upwards, over the long term,to either the potable ground water (usually near the surface) or to theatmosphere.

Carbon dioxide may be injected into different types of geologicalformations, e.g., depleted oil reservoirs, carbonate reservoirs, deepsaline aquifers and deep coal seams. (See Ashkan B et al (2013)“Simulation study of CO₂ sequestration potential of the Mary Lee coalzone, Black Warrior basin”. Environ Earth Sci 70:2501-2509; andWitkowski A, Majkut M, Rulik S (2014) “Analysis of pipelinetransportation systems for carbon dioxide sequestration”. Arch Thermodyn35:117-140, each incorporated herein by reference in their entirety).

In September 1996, the offshore gas field Sleipner, located in the NorthSea about 250 km west of Norway, started injecting 1 million tons ofcarbon dioxide into a saline aquifer at a depth of 1000 m. (See BaklidA, Korbol R, Owren G (1996) “Sleipner Vest CO₂ disposal, CO₂ injectioninto a shallow underground aquifer”. Soc Pet Eng.https://doi.org/10.2118/36600-MS; and Torp and Gale 2004, eachincorporated herein by reference in their entirety). Following theSleipner project, two more carbon dioxide sequestration projects wereinitiated in Canada and Algeria. In the Algerian gas project (In Salah),0.5-1 million tons of carbon dioxide were injected into a water-filledsandstone reservoir. The carbon dioxide injection continued for fiveyears, which caused a ground uplift of 5 mm per year, as measured bysatellite-based Interferometric Synthetic Aperture Radar (InSAR).(InSAR) measures ground displacement above the reservoir due to eitherinjection or production processes.

Further, more than 25 million tons of carbon dioxide is captured andstored annually in deep sedimentary reservoirs by 15 large-scale Carbondioxide Capture and Storage (CCS) projects. (See White DJ, Burrowes G,Davis T et al (2004) “Greenhouse gas sequestration in abandoned oilreservoirs: the International Energy Agency Weyburn pilot project”. GeolSoc Am 14(7):4-11; Rutqvist J, Vasco D W, Myer L (2010) “Coupledreservoir geo-mechanical analysis of CO₂ injection and grounddeformations at In Salah, Algeria”. Int J Greenhouse Gas Control4:225-230; Jin C, Liu L, Li Y, Zeng R (2017) “Capacity assessment of CO₂storage in deep saline aquifers by mineral trapping and the implicationsfor Songliao Basin”, Northeast China. Energy Sci Eng 5(2):81-89; andMahmoud M, Elkatatny S M (2017) “Dual benefit of CO₂ sequestration:storage and enhanced oil recovery”. Pet Petrochem Eng J 1(2):1-10, eachincorporated herein by reference in their entirety). The CCS process canbe viewed as a sink process, as it removes the greenhouse gases from theenvironment. (See Torvanger AK, Rypdal S (2005) “Geological CO₂ storageas a climate change mitigation option”. Mitig Adapt Strateg Glob Chang10(4):693-715, incorporated herein by reference in its entirety).

Several reported studies have addressed the pore pressure buildup duringcarbon dioxide injection and its effect on reservoir deformation, aswell as the reservoir's stability. In the case of In-Salah project inAlgeria, about 0.5-1 million tons of carbon dioxide was injected into awater-filled sandstone reservoir. The carbon dioxide injection wascontinued for five years, which caused huge pressure buildup in thereservoir and provoked a measurable ground uplift of 5 millimeters peryear. This excessive pressure buildup may cause horizontal stresses todecrease and can cause failure of the reservoir structure, including thecaprock. Both ground uplift during carbon dioxide injection and groundsubsidence during the oil and gas productions may affect theinfrastructure in the vicinity of the injection reservoir. (See JtirgenE S, Siggins F A, Brian J E (2005) “Predicting and monitoringgeo-mechanical effects of CO₂ injection”. Carbon dioxide capture forstorage in deep geologic formations 2:751-766; Moeck I, Kwiatek G,Zimmermann G (2009) “Slip tendency analysis, fault reactivationpotential and induced seismicity in a deep geothermal reservoir”.Journal of Structural Geology 10:1174-1182; Rutqvist J, Vasco D W, MyerL (2010) “Coupled reservoir geo-mechanical analysis of CO₂ injection andground deformations at In Salah, Algeria”. International Journal ofGreenhouse Gas Control 4:225-230; Rutqvist J, Rinaldi AP, Cappa F,Moridis G J (2013) “Modeling of fault reactivation and inducedseismicity during hydraulic fracturing of shale-gas reservoirs”. Journalof Petroleum Science and Engineering, 107:31-44; and Zhang H, Liu J,Elsworth D (2008) “How sorption-induced matrix deformation affects gasflow in Coal seams: a new FE model”. International Journal of RockMechanics and Mining Sciences 45(8):1226-1236, each incorporated hereinby reference in their entirety).

If the injected carbon dioxide can flow across the boundaries of thereservoir, then the open boundary conditions are normally used during amodeling procedure. For a reservoir with open boundary conditions, thepressure build-up will spread along the reservoir if the permeability ofthe reservoir is low and the carbon dioxide is injected at a highinjection rate. However, for reservoirs with closed boundary conditions,the injection of carbon dioxide results causes significant pressurebuildup and subsequent reduction in carbon dioxide storage capacity,thus posing great risk for geo-mechanical failure of the reservoir. (SeeEshiet K, Sheng Y (2014) “Investigation of geo-mechanical responses ofreservoirs induced by CO₂ storage”. Environmental Earth Sciences71:3999-4020; Khan S, Khulief Y A, Al-Shuhail AA (2017) “Numericalmodeling of the Geomechanical behavior of Biyadh reservoir undergoingCO₂ Injection”. International Journal of Geomechanics 17(8),10.1061/(ASCE)GM.1943-5622.0000893, 1-12; and Qu H Y, Liu J S, Pan Z J,Connell L (2010) “Impact of thermal processes on CO₂ injectivity into acoal seam”. In IOP Conference Series: Materials Science and Engineering,10.1088/1757-899X/10/1/012090, 1-10, each incorporated herein byreference in their entirety).

The change in permeability is highly dependent on the change in theeffective stresses and matrix swelling, which are also dependent on thetype of boundary conditions of the reservoir. Although the previouscited documents provide an insight into the changes in the localproperties of the reservoir, such as permeability and porosity fordifferent types of boundary conditions, a need remains to exploreoverall effects, e.g. ground uplift due to different types of boundaryconditions. (See Kiyama T et al (2011) “Coal swelling strain andpermeability change with injecting liquid/supercritical CO₂ and N₂ atstress-constrained conditions”. International Journal of Coal Geology85(1):56-64; Khan S, Al-Shuhail A A, Khulief Y A (2016). “Numericalmodeling of the geo-mechanical Behavior of Ghawar Arab-D carbonatepetroleum reservoir undergoing CO₂ injection”. Environmental EarthSciences Journal 75(1), 10.1007/s12665-016-6122-3, 1-15; and Zhang etal. 2008, each incorporated herein by reference in their entirety).

The Ghawar oil field in Saudi Arabia shown in FIG. 1 may be a goodcandidate for CO₂ sequestration once it is depleted as it has stablelayers. Additionally, The Ghawar oil field has been extensively loggedand the velocities, pore pressures, depths and lithography have alreadybeen determined. Ghawar is a large north-trending anticlinal structure,some 250 kilometers long and 30 kilometers wide. It is a drape fold overa basement horst, which grew initially during the CarboniferousHercynian deformation and was reactivated episodically, particularlyduring the Late Cretaceous. In detail, the deep structure consists ofseveral en echelon horst blocks that probably formed in response toright-lateral transpression. The bounding faults have throws exceeding3000 feet at the Silurian level but terminate within the Triassicsection. The episodic structural growth influenced sedimentation of thePermo-Carboniferous sandstone reservoirs, which on lap the structure andthe Jurassic and Permian carbonate reservoirs, which accumulated inshoals above structural culminations. The excellent reservoir quality isdue to the preservation of the primary porosity, the enhancement ofpermeability, and the presence of fractures in the deeper and tighterparts. Oil has been sourced exclusively from Jurassic organic-richmudstones and is effectively sealed beneath massive anhydrite. Thegeneral absence of faults at the Arab-D level has maintained sealintegrity. (See Afifi, A., “Ghawar: The Anatomy of the World's LargestOil Field”, Jan. 25, 2005. Search and Discovery Article #20026.http://www.searchanddiscovery.com/documents/2004/afifi01/, incorporatedherein by reference in its entirety.

Carbon dioxide nay also be stored in aquifers. An aquifer in a targetedunderground deep reservoir may contain saline water. When carbon dioxideis injected into the aquifer, water in the rock matrix is replaced bythe injected carbon dioxide. To increase the storage capacity of carbondioxide, the CO₂ is injected into a reservoir in its supercritical form.Carbon dioxide changes to its supercritical form when it is exposed to atemperature of 304.25 K and to a pressure of 7.39 MPa. In general,underground reservoirs at greater depths are less vulnerable to leakageof carbon dioxide into the environment. (See Jennifer S C, Azra N T(2015) “Coupled geomechanics and fluid flow model for productionoptimization in naturally fractured shale reservoirs”. SEG technicalprogram expanded abstracts 2015.https://doi.org/10.1190/segam2015-5928833.1. Accessed 09 September 2017;Gibbins J, Chalmers H (2008) “Carbon capture and storage”. Energ Policy36:4317-4322; Sung S P et al (2016) “Numerical modeling of the tensilefracture reactivation under the effects of rock geo-mechanicalproperties and heterogeneity during CO₂ storage”. Environ Earth Sci75:298-303; and Zhangshuan H et al (2012) “Evaluating the impact ofcaprock and reservoir properties on potential risk of CO₂ leakage afterinjection”. Environ Earth Sci 66:2403-2415, each incorporated herein byreference in their entirety).

The injection of carbon dioxide may affect the stability of thereservoir if the injected quantity is greater than the storage capacityof the reservoir. (See Sandrine V G, Nauroy J F, Brosse E (2009) “3Dgeo-mechanical modeling for CO₂ geologic storage in the Doggercarbonates of the Paris basin”. Int J Greenhouse Gas Control 3:288-299,incorporated herein by reference in its entirety). A key injectionparameter is the carbon dioxide injection pressure. An increase ininjection pressure increases the storage capacity of a reservoir. (SeeBustin R M, Clarkson C R (1998) “Geological controls on coal bed methanereservoir capacity and gas content”. Int J Coal Geol 38:3-26,incorporated herein by reference in its entirety). However, an excessiveincrease in the injection pressure and the subsequent change in thehorizontal stresses may result in failure of the reservoir structure andthe caprock, which is a geological layer normally of low permeabilitythat caps the reservoir. (See Engelder T, Fischer M P (1994) “Influenceof poroelastic behavior on the magnitude of minimum horizontal stress,S_(h), in over pressured parts of sedimentary basins”. Geology22:949-952, incorporated herein by reference in its entirety).Accordingly, safe injection parameters must be evaluated by performingcoupled geo-mechanical modeling of the reservoir. Geomechanical modelingduring carbon dioxide injection into a reservoir helps to evaluate thebehavior of the reservoir as the pressure and deformation fields changedue to the injection of carbon dioxide. (See Rutqvist J, Wu Y S, TsangCF, Bodvarsson G (2002) “A modeling approach for analysis of coupledmultiphase fluid flow, heat transfer, and deformation in fracturedporous rock”. Int J Rock Mech Min Sci 39:429-442, incorporated herein byreference in its entirety). Carbon dioxide injection in an Enhanced OilRecovery (EOR) is a process in which carbon dioxide or other fluid isinjected into a low-pressure oil containing reservoir to increasereservoir pressure and enhance oil production. (See Holloway S (1997)“An overview of the underground disposal of carbon dioxide”. EnergyConyers Manag 38: 193-198; Gibbins J, Haszeldine S, Holloway S et al(2006) “Scope for future CO₂ emission reductions from electricitygeneration through the deployment of carbon capture and storagetechnologies”. Cambridge University Press, United Kingdom; Gibbins J,Chalmers H (2007) “Preparing for global rollout: a “developed countryfirst” demonstration program for rapid CCS deployment”. Energy Policy,https://doi.org/10.1016/j.enol.2007.10.021; Gibbins and Chalmers (2008);and Wojtacki K, Lewandowska J, Gouze P, Lipkowski A (2015) “Numericalcomputations of rock dissolution and geo-mechanical effects for CO₂geological storage”. Int J Numer Anal Methods Geomech 39:482-506, eachincorporated herein by reference in their entirety).

Apart from coal beds and oil and gas reservoirs, carbon dioxide has beeninjected into saline aquifers, thus avoiding some of the organizationaldifficulties associated with Enhanced Oil and the Enhanced Coal BedMethane (ECBM) recovery processes in which carbon dioxide is injectedinto coal. The injected carbon dioxide is adsorbed onto the coal matrixand thus releases the methane from the rock matrix. The released methanecan be produced using a production well. (See Stevens S H, Kuuskraa V A,Gale J, Beecy D (2001) “CO₂ injection and sequestration in depleted oiland gas fields and deep coal seams: worldwide potential and costs”.Environ Geosci 8(3):200-209; Bachu S, Adams JJ (2003) “Sequestration ofCO₂ in geological media in response to climate change: capacity of deepsaline aquifers to sequester CO₂ in solution”. Energy Conyers Manag44(20):3151-3175; Damen K, Faaij A B, van Bergen F, Gale J, Lysen E(2005) “Identification of early opportunities for CO₂sequestration—worldwide screening for CO₂ EOR and CO₂-ECBM projects”.Energy 30(10): 1931-1952; and White C M, Smith D H, Jones K L, Goodman AL, Jikich S A, LaCount R B, DuBose S B, Ozdemir E, Morsi B I, SchroederK T (2005) “Sequestration of carbon dioxide in coal with enhanced coalbed methane recovery a review”. Energy Fuel 19(3):659-724, eachincorporated herein by reference in their entirety).

Carbon dioxide injection has been considered as a viable technique forenhanced oil recovery. Saudi Arabia has proposed utilizing CO₂ injectionin the Ghawar reservoir. The Ghawar oil field is primary composed ofcarbonate rock, which is a naturally fractured structure formed as aresult of the precipitation of calcium carbonate. In Saudi Arabia,almost 60% of the oil is found in the carbonate rocks. The injectedcarbon dioxide can flow both in the matrix pores and fractures in thecarbonate reservoir. Technical feasibility studies for carbon dioxidesequestration in some of the depleted oil reservoirs have beenperformed. In a depleted oil or gas reservoir, the magnitude of the porepressure is low due to the excessive production of oil and gas. (SeePollastro R M (2003) “Total petroleum systems of the Paleozoic andJurassic, Greater Ghawar uplift and adjoining provinces of central SaudiArabia and northern Arabian-Persian Gulf”. US Department of theInterior, US Geological Survey.https://pubs.er.usgs.gov/publication/b2202H. Accessed 9 Sep. 2017;Khalid A, Hussain M, Imam B et al (2004) “Lithologic characteristics anddiagnosis of the Devonian Jauf sandstone at Ghawar Field, Eastern SaudiArabia”. Mar Pet Geol 21:1221-1234; Abdulkader MA (2005) “Ghawar: theanatomy of the world's largest oil field”. Saudi Aramco search anddiscovery article#20026.http://www.searchanddiscovery.com/documents/2004/afifi01/. Accessed 26August 2017; and Swart P K, Cantrell D L, Westphal H, Handford C R,Kendall C G (2005) “Origin of dolomite in the Arab-D reservoir from theGhawar field, Saudi Arabia: evidence from petrographic and geochemicalconstraints”. J Sediment Res 75(3):476-491, each incorporated herein byreference in their entirety).

Apart from carbonate reservoirs, saline aquifers in particular, such asthe Biyadh sandstone reservoir, can be used to store carbon dioxide forlong periods of time. Sandstone rock is made of the sand-size rockgrains. Sandstone rocks have enough permeability and porosity to be usedfor carbon dioxide sequestration. For carbon dioxide sequestration insaline aquifers, a feasibility study was performed before starting theinjection process. (See Pruess K, Garcia J (2002) “Multiphase flowdynamics during CO₂ disposal into saline aquifers”. Environ Geol 42:282-295; Barnes D A, Bacon D H, Kelley S R (2009) “Geologicalsequestration of carbon dioxide in the Cambrian Mount Simon sandstone:regional storage capacity, site characterization, and large-scaleinjection feasibility”, Michigan Basin. Environ Geosci 16(3):163-183;Rayward WJ, Woods A W (2011) “Some implications of cold CO₂ injectioninto deep saline aquifers”. Geophys Res Lett 38(6):1-6,https://doi.org/10.1029/2010GL046412; Lamert H, Geistlinger H, Werban U,SchUtze C, Peter A, Hornbruch G, Schulz A, Pohlert M, Kalia S, Beyer M,GroBmann J, Dahmke A, Dietrich P (2012) “Feasibility of geoelectricalmonitoring and multiphase modeling for process understanding of gaseousCO₂ injection into a shallow aquifer”. Environ Earth Sci 67(2):447-462;Yang D X, Zeng R S, Zhang Y, Wang Z Q, Wang S, Jin C (2012) “Numericalsimulation of multiphase flows of CO₂ storage in saline aquifers inDaqingzijing oilfield, China”. Clean Techn Environ Policy 14(4):609-618;Zhang Z, Agarwal RK (2012) “Numerical simulation and optimization of CO₂sequestration in saline aquifers for vertical and horizontal wellinjection”. Comput Geosci 16(4):891-6899; and Zhao R, Cheng J (2015)“Non-isothermal modeling of CO₂ injection into saline aquifers at a lowtemperature”. Environ Earth Sci 73(9):5307-5316, each incorporatedherein by reference in their entirety).

During coupled geo-mechanical modeling, fluid flow in the reservoir aswell as deformation of the reservoir due to the fluid flow areparameters of note. Shale is fine-grained low-permeability rock thatnormally caps the oil and gas reservoirs. In the case of carbon dioxideinjection and sequestration, the shale rock cap will prevent the leakageof the stored carbon dioxide. The Biyadh sandstone reservoir is locatedbetween the Shale Hith Anhydrite and the Shuaiba layers. It is composedof highly impermeable layers, which can trap carbon dioxide for a longduration. The masking of Biyadh reservoir by the low permeabilityShuaiba, Wasia, and

Aruma sedimentary rocks ensures that the stored carbon dioxide will notleak to the surface or to the potable water layer of Um Ar Radhuma,which is located above the Biyadh reservoir. Attempts to model thetwo-phase flow in the Biyadh sandstone reservoir and its correspondingdeformation have been reported. (See Tran D, Nghiem L, Buchanan L (2005)“An overview of iterative coupling between geo-mechanical deformationand reservoir flow”. Soc Pet Eng.

https://doi.org/10.2118/97879-MS; Chen Z, Huan G, Ma Y (2006)“Computational methods for multiphase flows in porous media”. Siam,Germany; and Kvamme B, Liu S (2009) “Reactive transport of CO₂ in salineaquifers with implicit geo-mechanical analysis”. Energy Procedia1(1):3267-3274, each incorporated herein by reference in theirentirety). The depth of Biyadh reservoir at over 1000 meters has beendetermined to be sufficient for storing carbon dioxide in itssupercritical form, which serves to increase the storage capacity. Inaddition, the high permeability of Biyadh reservoir enhances the rapidcarbon dioxide transport within the reservoir. (See Kalbus E, Oswald S,Wang Wet al (2011) “Large-scale modeling of the groundwater resources onthe Arabian platform”. Int J Water Resour Arid Environ 1(1):38-47;Hakimi M H, Shalaby M R, Abdullah W H (2012) “Diagenetic characteristicsand reservoir quality of the lower cretaceous Biyadh sandstones atKharir oilfield in the western central Masila basin”, Yemen. J AsianEarth Sci 51:109-120; and Al-Shuhail A A, Alshuhail A A, Khulief Y A(2014) “CO₂ leakage detection using geophysical methods under aridnear-surface conditions: progress report of KACST TIC-CCS project numberTIC-CCS-1, Saudi Arabia”, each incorporated herein by reference in theirentirety).

The size of the reservoir used during the geo-mechanical modeling is arepresentative sample and not the actual size of the reservoir. Theselection of the reservoir size is also dependent on the mass of theinjected CO₂ per year. The geological sequestration of CO₂ was startedin 1996 by the Sleipner project in the North Sea, followed by the FennBig Valley and Weyburn projects in Canada. (See Gunter W D, Mayor M J,Robinson J R (2004) “CO₂ storage and enhanced methane production: fieldtesting at Fenn-Big Valley, Alberta, Canada, with application”.Proceedings of the 7th International Conference on Greenhouse GasControl Technologies (GHGT-7), Alberta, Canada, 413-422; and White D(2009) “Monitoring CO₂ storage during EOR at the Weyburn-Midale field”.Leading Edge 28:838-842, each incorporated herein by reference in theirentirety). Following these early carbon dioxide projects, the injectionof CO₂ was continued at the In-Salah project in Algeria, Frio project inUSA, and Qinshui Basin project in China. The above mentioned carbondioxide injection projects ranged from a pilot scale to large-scalecommercial projects, however, the effect of the selected reservoir sizeand boundary conditions on the pressure and deformation responses of thereservoir was not addressed in those studies. (See Kharaka Y K et al(2006) “Gas-water-rock interactions in sedimentary basins: CO₂sequestration in the Frio Formation, Texas, USA”. Journal of GeochemicalExploration 89:183-186; Metz B, Davidson O, de Coninck H, Loos M, MeyerL (2007) “A report on the Mitigation of Climate Change”. CambridgeUniversity Press; and Zhou F, Hou W, Allinson G, Wu J, Wang J, Cinar Y(2013) “A feasibility study of ECBM recovery and CO₂ storage for aproducing CBM field in Southeast Qinshui Basin, China”. InternationalJournal of Greenhouse Gas Control 10.1016/j.ijggc.2013.08.011, 26-40,each incorporated herein by reference in their entirety).

Although studies have been carried out to investigate the effects ofreservoir size and boundary conditions on pore pressure buildup duringcarbon dioxide injection, extensive research is needed to evaluate theeffects of reservoir size and boundary conditions on the ground uplift,fault reactivation, and stability of the reservoir, to avoid caprockfailure and the subsequent leakage of carbon dioxide to the overburdenlayers. (See Han W S, Kim K Y (2018) “Evaluation of CO₂ plume migrationand storage under dip and sinusoidal structures in geologic formation”.Journal of Petroleum Science and Engineering 169(1):760-771; Teletzke GF , Lu P (2013) “Guidelines for reservoir modeling of geologic CO₂storage”. Energy Procedia 37:3936-3944; and Zhang L, Dilmore R M,Bromhal G S (2016) “Effect of outer boundary condition, reservoir size,and CO₂ effective permeability on pressure and CO₂ saturationpredictions under carbon sequestration conditions”. Greenhouse Gases:Science and Technology 6(4):546-560, each incorporated herein byreference in their entirety).

None of the references cited above describes the combination ofdetermining pore pressure, horizontal stresses, and the vertical grounddisplacement caused by carbon dioxide injection, determining the effectof varying the injection well arrangement on the storage capacity andstability of the reservoir, and determining the relationship betweenreservoir size and boundary conditions on the ground uplift, faultreactivation, and stability of the reservoir, to avoid caprock failureand the subsequent leakage of carbon dioxide to the overburden layers.

Accordingly it is one objective of the present disclosure to provide adescription of a process for monitoring carbon dioxide injection andlong-time sequestration in reservoirs in order to avoid leakage ofcarbon dioxide through the caprock. In some aspects geo-mechanicalmodeling is used to estimate the safe injection parameters and take intoaccount the increase in the pore pressure, horizontal stresses, andvertical ground displacement caused by carbon dioxide injection.

It is another objective of the present disclosure to provide a methodfor reducing pore pressure build-up and maximizing reservoir storagecapacity by varying the number of carbon dioxide injection wells alongwith their placement arrangement in a naturally fractured reservoir.

It is another objective of the present disclosure to provide a methodfor relating reservoir boundary conditions to caprock uplift, porepressure buildup, fault reactivation and long term stability of CO₂sequestration.

SUMMARY

In an exemplary embodiment, a method for carbon dioxide sequestration ina geologic reservoir having a caprock and a plurality of subsurfacelayers between the reservoir and the caprock is described comprisingconstructing a reservoir model, varying injection pressures of CO2, thenumber of injection wells, the locations of the injection wells and anarray formation of the injection wells, the sizes of the model and theboundaries of the model to determine changes in changes in the porosity,the horizontal stresses, the pore pressures, the permeabilities, thepressure wave velocities and the shear wave velocities which affectfracturing, fracture reactivation and caprock uplift.

In another exemplary embodiment, an alarming system for leakage in ageologic reservoir sequestering carbon dioxide, the geologic reservoirhaving a caprock and a plurality of subsurface layers between thereservoir and the caprock includes a satellite surface imaging databaseincluding topology images of the geologic reservoir taken over a periodof time, a memory storing the satellite imaging database, a reservoirdatabase and program instructions, a computer comprising a processorwith circuitry configured to cause the one or more processor to performthe program instructions to construct a reservoir model which includesreservoir boundary conditions, a three dimensional size of thereservoir, faults in the reservoir, lithography, rock densities,porosities (Ø), and depths of the caprock and the plurality ofsubsurface layers, initial values of horizontal stresses (σ), volumetricstrain (εv), pore pressures, permeabilities (k0), pressure wavevelocities and shear wave velocities of the reservoir, the caprock andthe subsurface layers. The reservoir model further comprises a pluralityof injection wells located in an array formation in the reservoir, eachinjection well supplying carbon dioxide at a plurality of supercriticalinjection pressures and predicting, by the computer, changes in theporosity, the horizontal stresses, the pore pressures, thepermeabilities, the pressure wave velocities and the shear wavevelocities of the reservoir, the caprock and the subsurface layers,based on each supercritical injection pressure and predicting, by thecomputer, an amount of caprock uplift and a location of the caprockuplift at each injection pressure based on the changes. The alarmingsystem further includes comparing, by the computer, the topology imagesover discrete time periods to determine if the caprock uplift is greaterthan a threshold, if the caprock uplift is greater than the threshold,comparing at least one location of caprock uplift to the locations ofinjection wells from the reservoir model to determine at least oneinjection well near the caprock uplift, and displaying an alarm on adisplay of the computer which shows the locations of caprock uplift andthe at least one injection well near the caprock uplift.

In another exemplary embodiment, a non-transitory computer readablemedium having instructions stored therein that, when executed by one ormore processor, cause the one or more processors to perform a method formonitoring the sequestration of carbon dioxide in a geologic reservoirhaving a caprock and a plurality of subsurface layers between thereservoir and the caprock is described.

The foregoing general description of the illustrative embodiments andthe following detailed description thereof are merely exemplary aspectsof the teachings of this disclosure, and are not restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of this disclosure and many of theattendant advantages thereof will be readily obtained as the samebecomes better understood by reference to the following detaileddescription when considered in connection with the accompanyingdrawings, wherein:

FIG. 1 illustrates a geological model showing the locations of theBiyadh and Arab Jubaila target locations for carbon dioxide injectionand the geological layers above and below the Biyadh reservoir;

FIGS. 2A and 2B illustrate the simulation model for Biyadh reservoirwith the injection well at center of the reservoir using A. a CMG-GEMand model B. a COMSOL model;

FIG. 3 is a graph illustrating the relative permeability curves for CO₂injection into Biyadh reservoir;

FIG. 4 is a graph illustrating the mesh size dependence of pore pressurebuildup during carbon dioxide injection;

FIGS. 5A and 5B illustrate the carbon dioxide saturation in A. fracturedcaprock and B. non-fractured caprock;

FIGS. 6A and 6B illustrate the reservoir pressure response during CO₂injection for A. fractured caprock and B. non-fractured caprock;

FIGS. 7A and 7B are graphs illustrating the pore pressure variation for10-year of CO₂ injection period at various injection pressures for A.fractured caprock and B. non-fractured caprock;

FIG. 8 is a graph illustrating the pore pressure variation for the10-year CO₂ injection period at an injection pressure of 27 MPa forfractured and non-fractured caprocks;

FIGS. 9A-9C illustrate the reservoir pressure response during CO₂injection for A. after 2 years, B. after 6 years, and C. after 10 years;

FIG. 10 illustrates the reservoir pressure response at various injectionpressures during CO₂ injection;

FIGS. 11A-11C illustrate the pore pressure in Wasia overburden layer fora fractured zone spaced from the injection well A. at 200 m, B. at 400m, and C. at 600 m;

FIGS. 12A and 12B illustrate the ground uplift for A. non-fracturedcaprock and B. fracture at 200 m from the injection well;

FIGS. 13A and 13B illustrate the ground vertical displacement during CO₂injection for the 10-year injection period at different injectionpressures for A. fractured caprock and B. non-fractured caprock;

FIGS. 14A-14D illustrate the influence of fractured zone permeability onvertical ground uplift for A. 1 mDarcy, B. 25 mDarcy, C. 50 mDarcy, andD. 100 mDarcy;

FIGS. 15A-15C illustrate the ground uplift for a fractured zone spacedfrom the injection well A. at 200 m, B. at 400 m, and C. Aa 600 m;

FIG. 16 is a graph illustrating the ground uplift during CO₂ injectionfor the 10-year injection period at different injection pressures;

FIGS. 17A and 17B illustrate the stability of Biyadh reservoir duringcarbon dioxide injection. A. numerical modeling in CMG-GEM. B. numericalmodeling in COMSOL Multiphysics.

FIGS. 18A-18D illustrate the simulation models for the Ghawar Arab-Dcarbonate petroleum reservoir undergoing CO₂ injection, A. single wellB. two wells (in line) C. three wells (triangular) D. four wells(rectangular);

FIGS. 19A-19D illustrate the pressure variation for various periods ofCO₂ injection; FIG. 20 illustrates the vertical ground uplift after fiveyears of carbon dioxide injection;

FIGS. 21A-21D illustrate the pressure variation after five years ofcarbon dioxide injection using two injection wells, A. at 600 meters B.at 800 meters C. at 1,000 meters D. at 1,200 meters;

FIGS. 22A-22D illustrate the vertical ground uplift after five years ofCO₂ injection for two injection wells, A. at 600 meters B. at 800 metersC. at 1,000 meters D. at 1,200 meters;

FIGS. 23A-23H illustrate the pressure variation after five years of CO₂injection using three injection wells: A. at 300 m triangular B. at 400m triangular C. at 500 m triangular D. at 600 m triangular E. at 500 min-line F. at 600 m in-line G. at 700 m in-line H. at 800 m in-line;

FIGS. 24A-24H illustrate the vertical ground uplift after five years ofCO₂ injection for three injection wells, A. at 300 m triangular B. at400 m triangular C. at 500 m triangular D. at 600 m triangular E. at 500m in-line F. at 600 m in-line G.at 700 m in-line H. at 800 m in-line;

FIGS. 25A-25D illustrate the pressure variation after five years ofcarbon dioxide injection using four injection wells, A. at 400 meters,B. at 500 meters, C. at 600 meters and D. At 700 meters;

FIGS. 26A-26D illustrate the vertical ground uplift after five years ofCO₂ injection pressure for four injection wells, A. at 400 meters B. at500 meters C. at 600 meters D. at 700 meters;

FIGS. 27A-27C illustrate the maximum pore pressure for variousarrangements of injection wells, A. two injection wells B. threeinjection wells C. four injection wells;

FIG. 28 illustrates a geological map with orientation and location ofthe Biyadh and Arab Jubaila reservoirs;

FIG. 29 illustrates a geological map showing the Ghawar oil field;

FIG. 30A-30C illustrate A. the Ghawar field with five injection wells,B. the lithology for the Arab Jubaila reservoir, and C. the porosity andflow fractions of the zones (1-4) of the Arab-D field;

FIGS. 31A-31B illustrate the models for Biyadh reservoir A. small model(4000×2000) meters B. large model (10,000×10,000) meters;

FIGS. 32A-32D illustrate the models for Arab Jubaila reservoir formultiple injection wells of size A. (2800×1800) meters B. (3000×2000)meters C. (6000×4000) meters D. (9000×6000) meters;

FIGS. 33A-33B illustrates the simulation models for Biyadh reservoir A.small model (4000×2000) meters, B. large model (10,000×10,000) meters;

FIG. 34 illustrates the pore pressure buildup (in MPa) after ten yearsof carbon dioxide injection for the small reservoir model;

FIG. 35 illustrates the pore pressure buildup (in MPa) after ten yearsof carbon dioxide injection for the large reservoir model;

FIG. 36 illustrates the effect of injection pressure on the porepressure buildup during ten years of carbon dioxide injection for thesmall reservoir model;

FIG. 37 illustrates the effect of injection pressure on the porepressure buildup during ten years of carbon dioxide injection for thelarge reservoir model;

FIGS. 38A-38D illustrate the pore pressure buildup (in Pa) during carbondioxide injection into various sized reservoirs A. (2800×1800) meters B.(3000×2000) meters C. (6000×4000) meters, D. (9000×6000) meters;

FIG. 39 illustrates the effect of boundary conditions on the porepressure buildup during 10-year injection period for a small reservoirmodel with open boundary conditions;

FIG. 40 illustrates the effect of boundary conditions on the porepressure buildup during 10-year injection period for a large reservoirmodel with open boundary conditions;

FIGS. 41A-41C illustrate the ground uplift (in mm) for the smallreservoir model after various periods of carbon dioxide injection A.after 3-years B. after 6-years C. after 10-years;

FIGS. 42A-42C illustrate the ground uplift (in mm) for the largereservoir model after various periods of carbon dioxide injection A.after 3-years B. after 6-years C. after 10-years;

FIG. 43 illustrates the effect of injection pressure on the grounduplift for the small reservoir model after 10-year injection period;

FIG. 44 illustrates the effect of injection pressure on the grounduplift for the large reservoir model after 10-year injection period;

FIGS. 45A-45D illustrate the ground uplift (in mm) during carbon dioxideinjection into different size models: A. (2800×1800) meters B.(3000×2000) meters C. (6000×4000) meters D. (9000×6000) meters;

FIGS. 46A-46B illustrate the effect of boundary conditions on the grounduplift during ten years of carbon dioxide injection A. closed reservoirmodel B. open reservoir model;

FIGS. 47A-47D illustrate the carbon dioxide saturation in the reservoirand overburden layers after carbon dioxide injection: A. for small modelafter 5 years, B. for small model after 10 years, C. for large modelafter 5 years and D. for large model after 10 years;

FIG. 48A-48B illustrates the pore pressure in Wasia overburden layer fora fault zone spaced at 200 meters from the injection well: A. smallmodel B. large model;

FIG. 49 illustrates the effect of reservoir size on the stability of thereservoir during CO₂ injection.

FIG. 50 is an illustration of a non-limiting example of details ofcomputing hardware used in the computing system, according to certainembodiments.

FIG. 51 is an exemplary schematic diagram of a data processing systemused within the computing system, according to certain embodiments.

FIG. 52 is an exemplary schematic diagram of a processor used with thecomputing system, according to certain embodiments.

FIG. 53 is an illustration of a non-limiting example of distributedcomponents which may share processing with the controller, according tocertain embodiments.

DETAILED DESCRIPTION

In the drawings, like reference numerals designate identical orcorresponding parts throughout the several views. Further, as usedherein, the words “a,” “an” and the like generally carry a meaning of“one or more,” unless stated otherwise. The drawings are generally drawnto scale unless specified otherwise or illustrating schematic structuresor flowcharts.

Furthermore, the terms “approximately,” “approximate,” “about,” andsimilar terms generally refer to ranges that include the identifiedvalue within a margin of 20%, 10%, or preferably 5%, and any valuestherebetween.

Aspects of this disclosure are directed to a method for carbon dioxidesequestration in a geologic reservoir having a caprock and a pluralityof subsurface layers between the reservoir and the caprock, an alarmingsystem for leakage in a geologic reservoir sequestering carbon dioxide,the geologic reservoir having a caprock and a plurality of subsurfacelayers between the reservoir and the caprock and a non-transitorycomputer readable medium having instructions stored therein that, whenexecuted by one or more processors, cause the one or more processors toperform a method for monitoring the sequestration of carbon dioxide in ageologic reservoir having a caprock and a plurality of subsurface layersbetween the reservoir and the caprock.

Aspects of the present disclosure are described with respect to anon-limiting example of the Ghawar oil field. The Biyadh sandstonereservoir 114 (see FIG. 1) is a suitable site for the long terminjection of carbon dioxide because: (a) it is capped by the lowpermeability Shuaiba layer 122, and (b) it is far away from the potablewater Um Er Radhuma layer 124. However, the methods and systems of thepresent disclosure are not limited to a particular reservoir or locationand may be applied to any geologic reservoir.

An oil field is particularly suited for CO₂ sequestration as oil fieldsurveys before and during production have collected a preponderance ofdata regarding reservoir porosity, depth, lithography, vertical andhorizontal stresses and such like. This accumulated data is invaluablein predicting the effects of CO₂ sequestration has on the internalreservoirs of the oil field. For example, CO₂ injection into a reservoirmay cause uplift of the caprock, which could endanger buildings, treesand other ground structures. Further, if the reservoir fractures, CO₂may leak into a potable ground water reservoir above the injectedreservoir, causing algae growth and contamination of the water. Largefractures may endanger the stability of the oil field.

Additionally, CO₂ may be injected into a carbonate reservoir duringproduction to aid in forcing remaining oil from the porous rocks. Thisprocess sequesters the CO₂ and may aid in supporting the depletedreservoir structure.

In an aspect of the present disclosure, a method is described formodelling a reservoir in order to predict the effects on caprock uplift,reservoir stability and fracture reactivation during CO₂ injection. Themethod determines the number of injection wells and their placementwithin the reservoir needed to achieve the highest amount ofsequestration while minimizing pore pressures, internal stresses,reservoir stability, fracture reactivation and caprock uplift. Themethod further relates the reservoir boundary conditions to build up ofpore pressure, caprock uplift and long term stability of the CO₂sequestration.

In an aspect, a model is utilized which accounts for the two-phase flowassociated with the geo-mechanical behavior of the reservoir withrespect to caprock leakage. At the surface, CO₂ acts as a gas which islighter than water. At a depth greater than 800 meters, the CO₂ enters asecond phase, where it is denser and mixes with water. Injecting CO₂into a saline reservoir, such as the Biyadh reservoir 114 of the Ghawaroil field shown in FIG. 1, which is at a depth greater than 1000 meters,thus mixes the CO₂ with the saline water. The large amount of additionalCO₂ may swell the reservoir and cause caprock uplift or reactivate afracture the reservoir. A fracture in the subsurface areas above theBiyadh layer may allow CO₂ to leak upward, becoming less dense, to enterthe potable ground water of the Um Ar Radhuma reservoir.

In another aspect, the method incorporates rock permeability in theprediction of caprock uplift or leakage. The permeability of a rock isits ability to pass fluids. The reservoirs in which carbon dioxide isinjected should have sufficient permeability to allow the spread of theinjected carbon dioxide along the reservoir. The caprock is consideredto be a dual permeability medium when modeling the carbon dioxideleakage through the caprock. Dual-permeability models assume that theporous medium consists of two interacting regions, one associated withthe inter-aggregate, macropore, or fracture system, and one comprisingmicropores (or intra-aggregate pores) inside soil aggregates or the rockmatrix.

In order to evaluate the permeability, the method incorporates theBarton-Bandis model to relate the changes in the effective stresses dueto CO₂ injection to the caprock fracture permeability. According to theBarton-Bandis Model, the fracture permeability is a function of theeffective stresses on the fracture model. If the effective stresses aredecreased, the fracture permeability will increase. The Barton-Bandismodel is applied only to specific grid blocks of the model thatrepresent fractures in the caprock. Changes in the effective stresseswithin a fracture in the caprock because of injection and the resultingleakage of the stored carbon dioxide are incorporated in the model. Theensuing ground uplift caused by the leaked carbon dioxide is alsoincluded in the model, thus allowing the determination of the exactlocation and dimension of the fracture in the caprock in terms of thecalculated location and magnitude of the ground uplift. (See“Barton-Bandis Criterion Synopsis”, published by Researchgate, 2017,incorporated herein by reference in its entirety).

The Mohr-Coulomb criterion for shear failure is incorporated in themodel in order to predict the stability of the reservoir. TheMohr-Coulomb failure criterion is a mathematical model describing thefailure of materials such as rocks due to shear stresses as well asnormal stresses. The Mohr-Coulomb failure criterion represents thelinear envelope that is obtained from a plot of the shear strength of amaterial versus the applied normal stress.

The injection of carbon dioxide into a reservoir causes both the porepressure and stress fields to change. In the non-limiting example of theBiyadh sandstone reservoir, the reservoir is filled with water, thus theinjected carbon dioxide is stored mainly by displacing the water andpartially by dissolving in water. The increase in the pore pressureprimarily affects reservoir stability if the caprock is not fractured.However, if the caprock is fractured, then the increase in the porepressure tends to activate the already existing fractures in thecaprock, thus causing leakage of carbon dioxide into the overburdenlayers. Therefore, the methods of the present disclosure monitor thepore pressure and ground uplift during carbon dioxide injection. Anyleakage of carbon dioxide because of excessive pore pressure buildup orany damage to infrastructure because of excessive ground uplift mayviolate climate mitigation policies.

Aspects of the present disclosure relate the rate of injection of CO₂into a reservoir layer to pore pressure and effective stresses infractured and non-fractured layers. The pore pressure and effectivestresses are used to predict subsequent uplift of the caprock, leakageinto the subsurface layers and long term stability of the reservoir.

In an additional aspect of the present disclosure, a method is describedfor reducing pore pressure build-up and effective stresses and formaximizing the reservoir storage capacity by varying the number ofcarbon dioxide injection wells along with their placement arrangement(distance from a reservoir center) in a naturally fractured carbonatereservoir. An optimum arrangement is determined at which the porepressure attains the lowest value at the same injection pressure and forthe same injection period for a particular reservoir.

In an aspect of the present disclosure, the modelling predicts theeffect of using multiple injection wells. The pore pressure variationsfor various arrangements of injection wells may be determined. Theresulting ground surface vertical uplift, reservoir stability andmaximum occupancy for various arrangements of injection wells may bepredicted.

In a further aspect of the present disclosure, the effect of thereservoir size and boundary conditions selection are incorporated usinggeo-mechanical modeling of the reservoir undergoing carbon dioxideinjection. Relationships between reservoir size and boundary conditionsselection to reservoir pore pressure buildup, ground uplift, faultreactivation and reservoir stability are determined.

Another aspect of the present disclosure, fault reactivation modeling isperformed to evaluate the effects of reservoir size and boundaryconditions on fault reactivation in the reservoir.

In an aspect of the present disclosure, hydro-mechanical coupledgeo-mechanical modeling was performed for carbon dioxide injection intosmall and large models of a sandstone reservoir.

In an aspect of the present disclosure, the reservoir model may be usedto identify the location of a fracture post injection, the amount ofleakage, the location of a fracture or predict the amount of caprockuplift due to the leakage.

Finally, the method predicts the estimated safe values of the injectionparameters to furnish benchmark data for CO₂ injection and long termsequestration in the reservoir. An alarm may be generated when caprockuplift is detected.

In order to model a sandstone reservoir containing water, multiphaseflow, as well as corresponding deformation of the reservoir, must beconsidered. Coupled geo-mechanical and stability analyses are performed.

The Arab Jubaila reservoir 110 is a carbonate reservoir of the Ghawaroil field. This reservoir is used as a non-limiting example in someaspects of the present disclosure. The carbonate reservoir may have rockstructures comprising at least one of grainstone, packstone, wackestone,mudstone, bafflestone, bindstone, framestone, floatstone, rudstone andshale.

The first embodiment is drawn to a method for carbon dioxidesequestration in a geologic reservoir (112 or 114, FIG. 1) having acaprock 122 and a plurality of subsurface layers (124, 126, 128, 130,132, 134, 136) between the reservoir and the caprock as shown in FIG. 1,comprising constructing a reservoir model (see FIG. 2A, 2B, 18A-18D,31A-33B), by a computer (5000, FIG. 50) having program instructions (inCPU 5001), a display 5010 and a reservoir database (in memory 5002)stored therein that, when executed by one or more processors, causes theone or more processors to construct the reservoir model which includesreservoir boundary conditions, a three dimensional size of thereservoir, faults in the reservoir, lithography, rock densities,porosities (Ø), and depths of the caprock and the plurality ofsubsurface layers; initial values of the horizontal stresses (σ), thevolumetric strain (ε_(v)), the pore pressures, the permeabilities (k₀),the pressure wave velocities and the shear wave velocities of thereservoir, the caprock and the subsurface layers sourced from thedatabase memory; a plurality of injection wells located in an arrayformation (see FIG. 18A-18D), in the reservoir (see, for example, twoinjection wells 116 a and 116 b, FIG. 1), each injection well supplyingcarbon dioxide at a plurality of injection pressures. The injectionpressures vary depending on the type of reservoir, either saline 114 orcarbonate 110 (in the non-limiting example of the Ghawar oil field ofFIG. 1), and its depth (1000-1700 m in the non-limiting example of theGhawar oil field of FIG. 1). The injection pressure in a carbonate wellmay be in the range of 1800-5000 pounds per square inch gauge (psig). Ina carbonate well, the injection pressure may be selected from the rangeof 2000-500 psig.

The method continues by determining, by the computer, changes in theporosity, the horizontal stresses, the pore pressures, thepermeabilities, the pressure wave velocities and the shear wavevelocities of the reservoir, the caprock and the subsurface layers,based on each injection pressure and determining, by the computer, anamount of caprock uplift and the location of the caprock uplift at eachrate of injection based on the changes; determining, by the computer,each volume of carbon dioxide sequestered in the reservoir at eachinjection pressure after a period of time and correlating, by thecomputer, the injection pressure at each injection well after the periodof time to the amount of caprock uplift and the amount of carbon dioxidesequestered.

The method further comprises minimizing the caprock uplift andmaximizing the volume of carbon dioxide sequestered by adjusting thenumber of injection wells, the array formation and the injectionpressure at each injection well, and providing, on the display, arepresentation of the reservoir displaying the number of injectionwells, the array formation, the locations of caprock uplift and theinjection pressures at each injection well for the minimized caprockuplift and the maximized volume of carbon dioxide sequestered.

The reservoir may be a carbonate reservoir including at least one ofgrainstone, packstone, wackestone, mudstone, bafflestone, bindstone,framestone, floatstone, rudstone and shale.

The reservoir may be a sandstone reservoir including saline water andwherein the injected carbon dioxide dissolves in the saline water.

In the method, determining changes in the porosity is based onØ*=Ø(1−ε_(v)) where ε* is the changed porosity.

The program instructions include a Mohr-Coulomb failure criterion; andcalculating, by the computer, the Mohr-Coulomb failure criterionrepresenting a stability of the reservoir based on the changes in porepressures, horizontal stresses and volumetric strains and predictingsafe values of the injection pressures based on the Mohr-Coulomb failurecriterion.

The program instructions also include a Barton-Bandis model whichdetermines changes in the permeability of the caprock based on theBarton-Bandis model and wherein the computer identifies a fracture inthe caprock based on a rise in the permeability of the caprock.

The program instructions include a Warren and Root fracture model. Themethod includes determining, by the computer, changes in thepermeability of the fault based on the Warren and Root fracture model;and identifying a reactivation of the fault.

The method further comprises calculating carbon dioxide saturation inthe subsurface layers based on the changes in the permeability of thefault, determining the fault location and the fault dimensions andpredicting the amount of caprock uplift.

The reservoir boundary conditions are at least one of an open boundaryand a closed boundary, and the method includes adjusting the number ofinjection wells based on the reservoir boundary conditions or adjustingthe number of injection wells based on the three dimensional size of thereservoir.

The program instructions further include geo-mechanical modellinginstructions wherein the geo-mechanical modelling incorporates theinitial values of reservoir density, pressure wave velocity and shearwave velocity to calculate changes in the modulus of elasticity, theshear modulus, a modulus of rigidity and a bulk modulus due to theinjection pressures.

The method additionally includes performing post injection monitoring ofthe pore pressure in the subsurface layers; identifying carbon dioxideleakage from the reservoir based on decreased levels of the porepressures and providing a leakage alarm.

The method further comprises performing post injection monitoring of thecaprock uplift; identifying carbon dioxide leakage from the reservoirbased on caprock uplift; and generating, by the computer, a leakagealarm (see sound controller 5020 and speakers 5022, FIG. 50).

The second embodiment is drawn to an alarming system for leakage in ageologic reservoir (110 or 114, FIG. 1) sequestering carbon dioxide, thegeologic reservoir having a caprock 122 and a plurality of subsurfacelayers (124, 126, 128, 130, 132, 134, 136) between the reservoir and thecaprock, comprising a satellite surface imaging database 5003 (see FIG.50) including topology images of the geologic reservoir taken over aperiod of time; a memory storing the satellite imaging database, areservoir database and program instructions; constructing a reservoirmodel (see FIG. 2A, 2B, 18A-18D, 31A-33B), by a computer (5000, FIG. 50)having program instructions, a display 5010 and a reservoir database (inmemory 5002) stored therein that, when executed by one or moreprocessors, causes the one or more processors to construct the reservoirmodel which includes the reservoir boundary conditions, the threedimensional size of the reservoir, faults in the reservoir, lithography,rock densities, porosities (Ø), and depths of the caprock and theplurality of subsurface layers; initial values of the horizontalstresses (σ), the volumetric strain (ε_(v)), the pore pressures, thepermeabilities (k₀), the pressure wave velocities and the shear wavevelocities of the reservoir, the caprock and the subsurface layers. Thereservoir model further includes a plurality of injection wells (see,for example, two injection wells 116 a and 116 b, FIG. 1), located in anarray formation in the reservoir (see FIG. 18A-18D), each injection wellsupplying carbon dioxide at a plurality of injection pressures.

The alarming system further includes determining, by the computer,changes in the porosity, the horizontal stresses, the pore pressures,the permeabilities, the pressure wave velocities and the shear wavevelocities of the reservoir, the caprock and the subsurface layers,based on each injection pressure, determining an amount of caprockuplift and the location of the caprock uplift at each rate of injectionbased on the changes, determining each volume of carbon dioxidesequestered in the reservoir at each injection pressure after a periodof time and correlating the injection pressure at each injection wellafter the period of time to the amount of caprock uplift and the amountof carbon dioxide sequestered, comparing the caprock uplift after theperiod of time to a threshold and generating an alarm when the caprockuplift is greater than the threshold. The threshold is selected from thegroup consisting of 25 mm or less than 25 mm, preferably 20 mm, evenmore preferably 15 mm, even more preferably 10 mm or less than 10 mm,even more preferably 5 mm or less than 5 mm.

The period of time is selected from the range of one to one hundredyears, preferably one to fifty years, even more preferably one to twentyfive years and even more preferably one to ten years.

The alarming system further comprises responding to the alarm byadjusting the number of injection wells, the array formation and theinjection pressure at each injection well to minimize the caprock upliftand volume of carbon dioxide sequestered; and providing, on the display,a representation of the reservoir displaying the number of injectionwells, the array formation, the locations of caprock uplift and theinjection pressures at each injection well for the minimized caprockuplift and the maximized volume of carbon dioxide sequestered.

The third embodiment is drawn to a non-transitory computer readablemedium having instructions stored therein that, when executed by one ormore processors, cause the one or more processors to perform a methodfor monitoring the sequestration of carbon dioxide in a geologicreservoir (112 or 114, FIG. 1) having a caprock 122 and a plurality ofsubsurface layers (124, 126, 128, 130, 132, 134, 136) between thereservoir and the caprock, comprising constructing a reservoir model(see FIG. 2A, 2B, 18A-18D, 31A-33B), by a computer (5000, FIG. 50)having program instructions (in CPU 5001), a display 5010 and areservoir database (in memory 5002) stored therein that, when executedby one or more processors, causes the one or more processors toconstruct the reservoir model.

The reservoir model includes reservoir boundary conditions, a threedimensional size of the reservoir, faults in the reservoir, lithography,rock densities, porosities (Ø), and depths of the caprock and theplurality of subsurface layers; the initial values of the horizontalstresses (σ), the volumetric strain (ε_(v)), the pore pressures, thepermeabilities (k₀), the pressure wave velocities and the shear wavevelocities of the reservoir, the caprock and the subsurface layers; aplurality of injection wells (see, for example, two injection wells 116a and 116 b, FIG. 1) located in an array formation in the reservoir (seeFIG. 18A-18D), each injection well supplying carbon dioxide at aplurality of injection pressures.

The computer readable medium method further includes determining, by thecomputer, changes in the porosity, the horizontal stresses, the porepressures, the permeabilities, the pressure wave velocities and theshear wave velocities of the reservoir, the caprock and the subsurfacelayers, based on each injection pressure; determining, by the computer,an amount of caprock uplift and the location of the caprock uplift ateach rate of injection based on the changes; determining, by thecomputer, each volume of carbon dioxide sequestered in the reservoir ateach injection pressure after a period of time; correlating, by thecomputer, the injection pressure at each injection well after the periodof time to the amount of caprock uplift and the amount of carbon dioxidesequestered; minimizing the caprock uplift and maximizing the volume ofcarbon dioxide sequestered by adjusting the number of injection wells,the array formation and the injection pressure at each injection well;and providing, on the display, a representation of the reservoirdisplaying the number of injection wells, the array formation, thelocations of caprock uplift and the injection pressures at eachinjection well for the minimized caprock uplift and the maximized volumeof carbon dioxide sequestered.

The program instructions further include a Mohr-Coulomb failurecriterion; and calculating, by the computer, a Mohr-Coulomb failurecriterion representing a stability of the reservoir based on the changesin pore pressures, horizontal stresses and volumetric strains.

Two reservoirs in the Ghawar oil field are used in non-limiting examplesto describe the methods of the present disclosure. As shown in FIG. 1,starting from the top, the Quaternary deposits 122 consist of QuaternaryEolian and Sabkha deposits (fine sand) with an average P-wave velocityof 850 m/s and density of 1500 kg/m3 with variable thickness. The HofufDam Hadrukh 124 formation is made of marl, shale, sandstone, and chalkylimestone with an average P-wave velocity of 1830 m/s, density of 1870kg/m3 and average thickness of 150 m. The Dammam 126 formation consistsof limestone, dolomite, and shale with an average P-wave velocity of3110 m/s, density of 2280 kg/m3 and average thickness of 200 m. The Rus128 formation is dominantly anhydrite in the subsurface with an averageP-wave velocity of 4260 m/s, density of 2280 kg/m3 and average thicknessof 90 m.

The Umm Er Radhuma 130 formation mainly consists of dolomitic limestonewith an average P-wave velocity of 3310 m/s, density of 2020 kg/m³ andaverage thickness of 250 m. The Aruma 132 formation consists oflimestone, subordinate dolomite and shale with an average P-wavevelocity of 2730 m/s, density of 2090 kg/m³ and average thickness of 160m. The Wasia 134 formation is mainly sandstone with subordinate shaleand rare dolomitic lenses with an average P-wave velocity of 3230 m/s,density of 2270 kg/m³ and average thickness of 230 m. The Shuaiba 136formation is a limestone with an average P-wave velocity of 3010 m/s,density of 2030 kg/m³ and average thickness of 100 m. The Biyadh 114formation is dominantly sandstone having an average P-wave velocity of4040 m/s, density of 2360 kg/m³ and average thickness of 320 m. The Hithanhydrite 112 is an evaporite with an average P-wave velocity of 4750m/s, density of 1870 kg/m³ and average thickness of 100 m. The Arab 110formation consists of dolomitic limestone and some anhydrite with anaverage P-wave velocity of 5940 m/s, density of 2400 kg/m³ and averagethickness of 170 m. This layer is the most prolific reservoir in theMesozoic petroleum system.

Hanifa and Tuwaiq mountain 138 formation consists of organic-richcarbonate mudrocks with an average P-wave velocity of 4900 m/s, densityof 2890 kg/m³ and average thickness of 310 m. This formation has longbeen recognized as the source rock of the Mesozoic petroleum system.Dhruma 140 formation is a limestone with an average P-wave velocity of5030 m/s, density of 2450 kg/m³ and average thickness of 330 m. Marrat142 formation is mainly shale with subordinate sandstone having anaverage P-wave velocity of 5670 m/s, density of 2470 kg/m³ and averagethickness of 160 m. The Minjur 144 formation consists of sandstone withminor shale having an average P-wave velocity of 5150 m/s, density of2400 kg/m³ and average thickness of 200 m. The Jilh 146 formationconsists of dolomitic limestone with an average P-wave velocity of 4820m/s, density of 2400 kg/m³ and an average thickness of 300 m. The Sudair148 formation is a red and green shale with an average P-wave velocityof 5180 m/s, density of 2700 kg/m³ and average thickness of 140 m. TheKhuff 150 formation is a dolomitic limestone with an average P-wavevelocity of 4950 m/s, density of 2400 kg/m³ and average thickness of 400m. The Unayzah 152 formation is a sandstone layer with an average P-wavevelocity of 3750 m/s, density of 2400 kg/m³ and average thickness of 100m.

The Qusaiba 154 formation is shale with an average P-wave velocity of3760 m/s, density of 2350 kg/m³ and average thickness of 300 m. Thisformation is believed to be the main source rock for thePaleozoic-Mesozoic petroleum system. The Qasim 156 formation is composedof mainly siliciclastic sandstone and shale with an average P-wavevelocity of 4190 m/s, density of 2480 kg/m³ and average thickness of 400m. The Saq 158 formation is a sandstone layer with an average P-wavevelocity of 3680 m/s, density of 2380 kg/m³ and average thickness of 400m. The Precambrian 160 basement is composed of igneous and metamorphicrocks with an average P-wave velocity of 6380 m/s and density of 2800kg/m³. This is the lowermost layer in the model and is assumed as a halfspace with an infinite thickness. The P-wave velocities, S-wavevelocities, density and depths are summarized in Table 2.

Aspects of the present disclosure are described using the example ofinjection of carbon dioxide into a sandstone reservoir containing salinewater. However, the techniques of the present disclosure are not limitedto sandstone reservoirs, and may apply to depleted oil or gas reservoirsformed of carbonate rock or to coal reservoirs.

Details of the model used to perform the methods and embodiments of thepresent disclosure are presented below.

A computer system (5000, FIG. 50), as detailed below with respect toFIG. 50-53, includes circuitry having program instructions (in CPU5001), a display 5010 and a reservoir database (in memory 5002) storedtherein that, when executed by one or more processors, causes the one ormore processors to construct the reservoir model which includesreservoir boundary conditions, a three dimensional size of thereservoir, faults in the reservoir, lithography, rock densities,porosities (Ø), and depths of the caprock and the plurality ofsubsurface layers; initial values of the horizontal stresses (σ), thevolumetric strain (ε_(v)), the pore pressures, the permeabilities (k₀),the pressure wave velocities and the shear wave velocities of thereservoir, the caprock and the subsurface layers sourced from thedatabase memory; a plurality of injection wells located in an arrayformation (see FIG. 18A-18D), in the reservoir (see, for example, twoinjection wells 116 a and 116 b, FIG. 1), each injection well supplyingcarbon dioxide at a plurality of injection pressures. The database holdsvalues for the reservoir boundary conditions, a three dimensional sizeof the reservoir, faults in the reservoir, lithography, rock densities,porosities (Ø), and depths of the caprock and the plurality ofsubsurface layers; initial values of the horizontal stresses (σ), thevolumetric strain (ε_(v)), the pore pressures, the permeabilities (k₀),the pressure wave velocities and the shear wave velocities of thereservoir. The processors of the computer system are configured todetermine changes in the porosity, the horizontal stresses, the porepressures, the permeabilities, the pressure wave velocities and theshear wave velocities of the reservoir, the caprock and the subsurfacelayers, based on each injection pressure and determining, by thecomputer, an amount of caprock uplift and the location of the caprockuplift at each rate of injection based on the changes; determining, bythe computer, each volume of carbon dioxide sequestered in the reservoirat each injection pressure after a period of time and correlating, bythe computer, the injection pressure at each injection well after theperiod of time to the amount of caprock uplift and the amount of carbondioxide sequestered.

An iterative coupling method is used in the to perform the coupledmultiphase flow and the reservoir deformation analyses. During iterativecoupling, the geo-mechanical calculations are not performed at the sametime as the reservoir flow calculations but are calculated one stepbehind. Equation-based modelling in COMSOL multi-physics finite elementsoftware is utilized for the numerical modelling of various carbondioxide injection scenarios. In this context, the effects of varying thenumber of injection wells together with their distances from thereservoir's center on the pattern of stress build-up and stability ofthe reservoir are investigated numerically. The simulation results showthat the storage capacity of the reservoir is highly affected bychanging the number and arrangement of injection wells, while showingdifferent stability margins for different injection well arrangements.Moreover, the results suggest the existence of an optimum arrangement atwhich the pore pressure attains the lowest value at the same injectionpressure and for the same injection period. In the iterative couplingmethod, the flow variable, e.g., pressure, is first calculated in theparent CMG flow simulator and then sent to the GEM module to calculatethe deformation variables, such as displacements, stresses, and strains.In the coupled geo-mechanical modeling by CMG-GEM, the displacementvalues in each time step are used to calculate the change in the matrixporosity. Using the change in porosity, a new value of the porosity ateach grid point is calculated and used for the next time step by theflow simulator. (See Kazemi et al. 1978; Barton C A, Zoback M D, Moos D(1995) “Fluid flow along potentially active faults in crystalline rock”.Geology 23(8):683-686; Anjani and Varun 1998; Tran D, Buchanan W L,Nghiem L X (2010) “Improved gridding technique for coupling geomechanicsto reservoir flow”. SPE J 15(1):64-75; Sahimi M (2011) “Flow andtransport in porous media and fractured rock: from classical methods tomodern approaches”. John Wiley & Sons, Germany; and “GEM AdvancedCompositional Reservoir Simulator, Version (2012) User guide”. Calgary.https://www.cmgl. ca/gem. Accessed 9 Sep. 2017; “Numerical modeling offracture permeability change in naturally fractured reservoirs using afully coupled displacement discontinuity method”. Dissertation. TexasA&M University, each incorporated herein by reference in theirentirety).

Equations for the multiphase flow, the deformation of the reservoir, andthe Barton-Bandis model of carbon dioxide leakage through the caprockare described below.

The fully coupled carbon dioxide flow and reservoir deformation modelsare generated in the COMSOL multiphysics software, wherein the MATLABcode has been utilized to generate the input properties of the rock ateach node of the reservoir's model.

The multiphase flow of carbon dioxide through the reservoir is simulatedby a compositional simulator. In a non-limiting example, the GEM flowsimulator is used. The composition of the phase is permitted to changedue to the variations in pressure and quantity of the injected fluid. Acompositional reservoir simulator calculates thePressure-Volume-Temperature (PVT) properties of oil and gas phases oncethey have been fitted to an equation of state (EOS), as a mixture ofcomponents. An Equation of State (EOS) is a simplified mathematicalmodel that calculates the phase behavior of the reservoir. In the caseof carbon dioxide injection into the reservoir, the conservation of massis defined as follows:

$\begin{matrix}{{{\frac{\partial\;}{\partial t}\left( {\rho_{L}{\varnothing\left( {1 - ɛ_{V}} \right)}S_{L}} \right)} - {\nabla{\cdot \left( {\rho_{L}v_{L}} \right)}}} = Q_{L}} & (1)\end{matrix}$where L refers to the phase (either water or carbon dioxide), ρ_(L) isthe density of corresponding phase, Ø is the true porosity of thereservoir, ε_(v) is the volumetric strain in the reservoir caused by theinjected carbon dioxide, S_(L) is the saturation, v_(L) representsDarcy's velocities, and Q_(L) represents the flow rate. (See Tore B,Eyvind A, Elin S (2009) “Safe storage parameters during CO₂ injectionusing coupled reservoir geo-mechanical analysis”. Excerpt from theProceedings of the COMSOL Conference Milan; “GEM Advanced CompositionalReservoir Simulator 2012”; and Amirlatifi A (2013) “Coupledgeo-mechanical reservoir simulation”. Dissertation. Missouri Universityof Science and Technology, each incorporated herein by reference intheir entirety). Equation (1) relates the deformation and porosity tothe injection of carbon dioxide at a specific flow rate into thereservoir. In this coupled model solution, new values of the porosityand volumetric strain are determined at each iteration step, in order tocope with the deformation of the reservoir. In this analysis, thereservoir's porosity (Ø*) is a function of both the true porosity (Ø)and the volumetric strain, which is defined as follows:Ø*=Ø(1−ε_(v))   (2)where ε_(v) is the volumetric strain. The new values of porosity, ascalculated by Eq. (2), are utilized by the modeling scheme to find thenew values of the pore pressure at each node. The values of the porepressure are used in the deformation equations to find the new values ofthe effective stresses. Knowing that the current value of porosity atany time step is dependent on the volumetric strain, Eq. (2) is used towrite the equation of the conservation of mass in the reservoir asfollows:

$\begin{matrix}{{{\frac{\partial\;}{\partial t}\left( {\rho_{L}\varnothing^{*}S_{L}} \right)} - {\nabla{\cdot \left( {\rho_{L}v_{L}} \right)}}} = Q_{L}} & (3)\end{matrix}$

Utilizing the current values of porosity, the method proceeds bycalculating new values of the pore pressure based on the saturation andcapillary pressure of each phase in the reservoir. The relations showingthe saturations and capillary pressure of carbon dioxide and water inthe reservoir can be stated as follows:S _(water) +S _(carbon dioxide)=1   (4)P _(c)(S _(water))=P _(carbon dioxide) −P _(water)   (5)where S_(water) is the saturation of water and S_(carbon dioxide) is thesaturation of carbon dioxide. As shown by Eq. (5), the capillarypressure P_(c) (S_(water)) is equal to the difference between the porepressures of carbon dioxide and water phases, respectively.

Darcy's law states that the velocity at which the injected fluid willflow in a reservoir is dependent on the pressure difference in thedirection of flow. Utilizing Darcy's law, the Darcy velocities for phaseL are given by the following:

$\begin{matrix}{{\nu\; L} = {\left( \frac{kL}{\mu L} \right)\left( {{\nabla p} - {\rho Lg}} \right)}} & (6)\end{matrix}$where k_(L) is the reservoir's permeability, μ_(L) is the viscosity, andp is the pore pressure. The permeability is updated at each time step,throughout the injection process. The new values of the reservoir'spermeability are calculated from the current values of the porosityusing the Kozeny-Carman model as follows:

$\begin{matrix}{\frac{k}{k_{o}} = {\left( \frac{\varnothing}{\varnothing_{o}} \right)^{3}\left( \frac{1 - \varnothing_{o}}{1 - \varnothing} \right)^{2}}} & (7)\end{matrix}$where k is the current value of permeability, k_(o) is the initialreservoir permeability, Ø is the current value of the porosity, andØ_(o) is the initial porosity of the reservoir. The Kozeny-Carman modeldetermines the value of the reservoir current permeability based on thevalue of the current porosity.

The deformation of the reservoir due to CO₂ injection is describedbelow.

The pressure-induced deformation of the reservoir due to CO₂ injectioncauses the displacement field to change. The new values of the straintensor may be calculated at each time step using the strain—displacementrelationship as follows:ε^(ij)=½(ui,j+uj,i)   (8)where u_(i, j) and ε_(ij) are the displacement and strain tensors,respectively. (See Mase G E (1970) “Theory and problems of continuummechanics”. Schaum's outline series, United States of America,incorporated herein by reference in its entirety). Using theconstitutive relation of Eq. (9) below, the stresses in the reservoircan be calculated from the already calculated strains using Eq. (8).This can be expressed as follows:

$\begin{matrix}{\sigma_{ij} = {{2G\; ɛ_{ij}} + {\left( {K - \frac{2G}{3}} \right)ɛ_{kk}\delta_{ij}} + {\alpha\; p\;\delta_{ij}}}} & (9)\end{matrix}$where σ_(ij) is the stress tensor, G is the shear modulus, K is the bulkmodulus, δ_(ij) is the Kronecker delta, and α is the Biot's coefficient.(See Mase (1970); Chen W F, Saleeb A F (1982) “Constitutive equationsfor engineering materials”. Wiley, N.Y., incorporated herein byreference in their entirety).

Once the new values of pore pressure and the total stresses aredetermined, the effective stresses in the reservoir can be easilycalculated. The effective stresses in the reservoir are defined asfollows:σ_(ij)′=σ_(ij)−αpδ_(ij)   (10)where α_(ij)′ represents the effective stresses. The effective stressescalculated from Eq. (10) are then used to perform stability analysis ofthe reservoir.

In the present disclosure, the carbon dioxide flow and the deformationequations presented above are coupled to give the changes in porepressure, effective stresses, and deformations. The change in theeffective stresses is utilized by the Barton-Bandis model to monitorcarbon dioxide leakage during the injection process by calculating thevalue of fracture permeability from the normal fracture effectivestress. The Barton-Bandis model accurately represents the change in thefracture permeability by considering its initial value at theequilibrium condition before carbon dioxide injection. As the effectivestresses start to decrease during carbon dioxide injection, the fracturepermeability increases. When the effective stresses decrease past acritical value, the fracture permeability becomes very high, thuscausing the fracture to open completely and leak the injected carbondioxide into the overburden layers. In comparison to other models usedfor calculating the fracture permeability, the Barton-Bandis model canbe applied to specific grid blocks in order to simulate the change inthe permeability of a single fracture. (See Warren J E, Root P J (1963)“The behavior of naturally fractured reservoirs”. Soc Pet Eng 3:245-255;Ameen M S, Smart B G D, Somerville J M, Hammilton S, Naji N A (2009)“Predicting rock mechanical properties of carbonates from wireline logs(a case study: Arab-D reservoir, Ghawar field, Saudi Arabia)”. Mar PetGeol 26:430-444; and Wu Y, Liu J, Elsworth D (2010) “Dual poroelasticresponse of a coal seam to CO₂ injection”. Int J Greenhouse Gas Control4:668-678, each incorporated herein by reference in their entirety).

The fracture permeability k_(f) is calculated as follows:k _(f) =k (e/e _(o))⁴   (11)where k is the fracture closure permeability. The following equationsare defined:

$\begin{matrix}{e = {e_{o} - V_{j}}} & (12) \\{V_{j} = \frac{\sigma_{n^{\prime}}}{\xi + {\sigma_{n^{\prime}}/V_{m}}}} & (13) \\{V_{m} = {e_{o}\left\lbrack {1 - \left( \frac{\lambda}{\overset{\_}{k}} \right)^{1/4}} \right\rbrack}} & (14)\end{matrix}$where e_(o) is the initial fracture aperture and e is the currentfracture aperture, V_(j) is the stress to fracture stiffness ratio, σ′is the normal fracture effective stress, ξ is the initial normalfracture stiffness, λ is the initial fracture permeability, and V_(m) isthe minimum fracture aperture.

The model description and input parameters are described below.

In a non-limiting example, CMG-GEM software has been employed formodeling the coupled multi-phase flow and deformation for thenon-limiting example of the Biyadh sandstone reservoir.

The model incorporates coupled geo-mechanical modelling and simulationto analyze stability. In a non-limiting example, the coupledgeo-mechanical modelling and simulation are performed using both theCMG-GEM (Computer Modeling Group Ltd.-Geomechanical Modeling Software)and COMSOL (cross-platform finite element solver and multiphysicssimulation software) have been utilized. COMSOL allows conventionalphysics-based user interfaces and coupled systems of partialdifferential equations. COMSOL and CMG-GEM are multiphysics softwarewhich may be used to model the flow of a fluid in the reservoir and theaccompanying deformation of the reservoir. GEM is an efficient,multidimensional, Equation-Of-State (EOS) simulator that provides theflexibility to use custom script files for performing multiphysicsoperations. An Equation of State (EOS) is a simplified mathematicalmodel that calculates the phase behavior of the reservoir.

GEM was developed by the Computer Modeling Group (CMG) for thegeo-mechanical modeling of single-porosity and naturally fracturedreservoirs. GEM can perform efficient dual permeability modeling byconsidering fluid flow, not only between the matrix elements, but alsobetween the matrix and fractures. One of the advantages of this softwareis its capability for simultaneous modeling of the production andinjection processes. It can also model the reservoir's post-productionand post-injection responses. COMSOL multiphysics software can also beused to perform equation-based modeling in which a recent set ofequations can be used for the gas flow and reservoir deformation. (SeeKazemi H, Vestal C R, Shank D G (1978) “An efficient multi componentnumerical simulator”. Soc Pet Eng J 18(5): 355-368; and Anjani K, VarunP (1998) “The role of coupled geo-mechanical modeling in reservoirsimulation Calgary, Alberta”.https://www.cmgl.ca/events/webinar-coupled-geomechanics. Accessed 8 Jun.2017, each incorporated herein by reference in their entirety).

The method focuses on determining the changes in the pore pressure andground uplift caused by carbon dioxide injection into the reservoir. TheBiyadh sandstone reservoir 114 is located above the Arab Jubailacarbonate reservoir 110 as shown in FIG. 1. The geological locations anddetails of different geological layers, which are stacked above andbelow the Biyadh reservoir are shown. Two injection wells (116 a, 116 b)are shown drilled through the rock layers. Tables 1 and 2 list theparameters used to model the reservoir.

As shown in FIG. 2A, 2B, simulation models were constructed for Biyadhsandstone reservoir in both the CMG-GEM (FIG. 2A) and COMSOL (FIG. 2B)software, wherein the injection well is located at the center of thereservoir. The three-dimensional-layered models of FIG. 2A, 2B representone under burden layer, a caprock above the Biyadh layer, and sixoverburden layers.

In this coupled geo-mechanical modeling procedure, the Biyadh reservoir114 was treated as a single-porosity structure, while the caprock 122was modeled as a fractured structure. The dual permeability modeling inCMG-GEM was performed with the fracture grid blocks activated only inthe caprock structure. The number of grid blocks of the caprock wasrefined to accurately simulate the fluid flow through the fractures. Atotal of 19,200 grid blocks were used to construct the model with theCartesian grid type. In the caprock, the Barton-Bandis model was used tocalculate the changes in the fracture permeability. An injectionpressure of 23 MPa was used to inject carbon dioxide for a period of tenyears. All sides of the model were assigned roller boundary conditions,except for the top side which is permitted to move in the upwarddirection.

Appropriate initial stresses were applied to the reservoir before theonset of carbon dioxide injection. Initial stresses were assigned to themodel both in the horizontal and vertical directions. The stresseschange with an increase in the depth below the ground level, based onthe depth and density of different layers in the overburden side of thereservoir. As the Biyadh formation is under compressional stress regime,the relationship between the magnitudes of the three principal stressesis such that, σ₁>σ₂>σ₃, where σ₁ is the maximum horizontal stress(σ_(H)), σ₂ is the minimum horizontal stress (σ_(h)), and σ₃ is thevertical stress (σ_(v)) caused by the weight of the overburden layers.The vertical stress is also known as lithostatic pressure and it is dueto the weight of the overburden layers (124, 126, 128, 130, 132, 134,136). The carbon dioxide injection pressure should always be less thanthe lithostatic pressure to avoid the failure of the reservoirstructure. (See Buchmann T, Connolly P (2007) “Contemporary kinematicsof the Upper Rhine graben: a 3D finite element approach”. Glob PlanetChang 58:287-309; Eckert A, Connolly A (2007) “Stress and fluid-flowinteraction for the geothermal field derived from 3D numerical models”.Geotherm Resour Counc Trans 31:385-390; and Hergert T, Heidbach O 2011)“Geomechanical model of the Marmara sea region-II, 3-D contemporarybackground stress field”. Int J Geophys 185:1090-1120, each incorporatedherein by reference in their entirety). The initial stresses wereapplied in all the three directions to all the layers of the model alongthe depth. The relationship between the horizontal and vertical stressesused is given by:σ_(Horizontal stress)=1.25σ_(vertical stress)   (15)

The 3D-layered model constructed in COMSOL to represent the Biyadhreservoir is shown in FIG. 2B. Knowing the average thickness of eachgeological layer, the model was constructed layer by layer in COMSOLusing a total of 60,685 grid blocks with the associated tetrahedralelements. One injection well with a specific diameter has been used toinject carbon dioxide at the center of the reservoir. The injectionpressure and flow rate were defined at the bottom hole side of theinjection well. As the injection of carbon dioxide was continued, thepore pressure increased in the reservoir, which caused vertical grounduplift. The input parameters used during the modeling are listed inTable 1. (See Ameen et al. (2009); Hakimi et al. (2012); Al-Shuhail etal. (2014); Eshiet K, Sheng Y (2014) “Investigation of geo-mechanicalresponses of reservoirs induced by CO₂ storage”. Environ Earth Sci71:3999-4020; Robert H, Mark Z (2014) “Adsorption of methane and carbondioxide on gas shale and pure mineral samples”. J Unconv Oil Gas Resour8:14-24; Tan X, Heinz K (2014) “Numerical study of variation in Biot'scoefficient with respect to microstructure of rocks”. Tectonophysics61:159-171; and Gameil M, Abdelbaset S (2015) “Gastropods from theCampanian Maastrichtian Aruma formation”, Central Saudi Arabia. J AfrEarth Sci 103:128-139, each incorporated herein by reference in theirentirety).

The method used for the calculation of the rock mass properties is basedon the rock density, pressure wave velocity, Poisson's ratio, and shearwave velocity as shown for the reservoir layers in the columns ofTable 1. Calculations of the rock properties, such as modulus ofelasticity, modulus of rigidity, and bulk modulus, the initial values ofrock porosity and permeability were determined based on mathematicalrelations given by Ameen et al. (2009), Hakimi et al. (2012), Al-Shuhailet al. (2014), Eshiet and Sheng (2014), Robert and Mark (2014), Tan andHeinz (2014), and Gameil and Abdelbaset (2015).

TABLE 1 Input parameters for coupled geo-mechanical modeling of Biyadhreservoir Hofuf Dam Rus Um Er Biyadh Hith Property Hadrukh DammamAnhydrite Radhuma Aruma Wasia Shuaiba Sulay Anhydrite Layer 150 200 90250 160 230 100 320 100 thickness (m) Grid top 0 150 350 440 690 8501080 1180 1500 (m) Rock 1877 2289 2280 2020 2090 2270 2030 2360 2960density ρ(kg/m³) Young's 7 21.43 37.25 21 15.6 27.84 18.1 44.7 42.67modulus, E (GPa) Bulk 2.83 11.47 22.8 11.67 7.8 9.82 9.13 25.7 38.2modulus, K (GPa) Shear 2.6 8.004 13.91 7.83 5.828 10.4 6.65 17.2 15.932modulus, G (GPa) Initial 0.2 0.2 0.28 0.24 0.17 0.29 0.09 0.12 0.01porosity, Ø_(n) Initial 0.2 0.02 0.25 0.01 0.15 0.2 0.025 0.7 0.00001permeability, km (10⁻¹⁵ m²) Pressure 1835 3110 4260 3310 2730 3230 30104040 4480 wave velocity, V_(p) (m/s) Shear 1180 1870 2470 1970 1670 21401810 2700 2320 wave velocity, V_(s) (m/s)

TABLE 2 Velocities and Pore Pressures of Layers of the Ghawar Oil FieldAvg. Vp Vs ρ Depth LAYER (km/s) (km/s) (gm/cc) (m) Eolian And 0.85 0.51.5 Variable Sabkha Hofufu Dam 1.83 1.17 1.87 150 Hadrukh Damman 3.111.86 2.28 200 Rus Anhydrite 4.26 2.47 2.28 90 Um Er Radhuma 3.31 1.972.02 250 Aruma 2.73 1.67 2.09 160 Wasia 3.23 2.14 2.27 230 Shuaiba 3.011.51 2.03 100 Biyadh Sulay 4.04 2.7 2.36 320 Hith Anhydrite 4.75 2.721.87 100 Arab Jubaila 5.94 3.04 2.74 170 Hanifa Tuwaiq 4.9 2.8 2.45 310Mountain Druma 5.03 2.86 2.45 330 Marrat 5.67 3.74 2.47 160 Minjur 5.152.76 2.4 200 Jilh 4.82 2.76 2.4 300 Sudair 5.18 2.67 2.7 140 Khuff 4.952.53 2.4 400 Unayzah 3.75 2.08 2.4 100 Qusaiba 3.76 2.5 2.35 300 Qasim4.19 2.14 2.48 400 Saq 3.68 2.45 2.38 400 Precambrian 6.38 2.45 2.8Infinite Basement

The values listed in Tables 1 and 2 may be obtained by various types ofwell logging. For example, rock density and strata velocities can bemeasured by seismic logging and ultrasonic logging, porosity can bemeasured by compensated neutron logging data, and the Young's, bulk andshear moduli can be calculated from the velocity, porosity and densitymeasurements. (See Boonyasatphan, P. “Reservoir Characterization ForUnconventional Resource Potential, Pitsanulok Basin, Onshore Thailand”,2017,https://mountainscholar.org/bitstream/handle/11124/171012/Boonyasatphan_mines-0052N_11268.pdf?sequence=1, incorporated herein by reference in its entirety).

CO₂ is injected into a water-filled medium in the Biyadh reservoir. Ascarbon dioxide is injected into the reservoir, it displaces the water inthe pores and increases the gas saturation in the vicinity of theinjection port. The relative permeability curves take into account thereservoir's pressure, temperature, and brine salinity. During the flowof a wetting and non-wetting phase in a reservoir rock, the pathfollowed by each phase is different. The two phases are distributedbased on their wetting characteristics which results in wetting andnon-wetting phase-relative permeability curves. (See Bennion B, Bachu S(2005) “Relative permeability characteristics for supercritical CO₂displacing water in a variety of potential sequestration zones”. In SPEAnnual Technical Conference and Exhibition. Society of PetroleumEngineers; and Bennion B, Bachu S (2006) “Dependence on temperature,pressure, and salinity of the IFT and relative permeability displacementcharacteristics of CO₂ injected in deep saline aquifers”. In SPE AnnualTechnical Conference and Exhibition, each incorporated herein byreference in their entirety). These curves are shown in FIG. 3. The meshdependency is shown in FIG. 4. The solution was shown to converge toconstant value as the grid density was increased beyond the normal gridsize, which was consequently adopted in the numerical modeling.

The model incorporates the variation in reservoir pore pressurevariation with CO₂ injection as shown below.

In order to investigate the effect of fracture on the pressure responsein the reservoir, a fractured zone was created in the caprock, byassigning a large value of permeability to the grid blocks at a distanceof 200 m from the injection well. The transport of carbon dioxide to theoverburden layers is restricted by the impermeable caprock. Thesimulation results of carbon dioxide saturation are shown for the casesof fractured (FIG. 5A) and non-fractured caprock (FIG. 5B). For the caseof non-fractured caprock, carbon dioxide was shown to have beenrestricted by the caprock to spread only within the reservoir, whereasfor the case of fractured caprock, the carbon dioxide leaked into theoverburden layers. As shown in FIG. 5A, the injection of carbon dioxideinto the reservoir at 520 tends to increase the pore pressure in thereservoir, thus opening the already existing fractures in the caprock.When the fractures in the caprock open up, carbon dioxide leaks to theoverburden layers 518. In the case of non-fractured caprock shown inFIG. 5B, the injection of carbon dioxide tends to increase the porepressure in the reservoir but spreads only within the reservoir.

The effect of carbon dioxide leakage can be seen in the pressureresponse of the reservoir. The pressure response of the reservoir isshown for the fractured (FIG. 6A) and non-fractured (FIG. 6B) caprocks.The injection increases the pore pressure in the reservoir, whichreaches values above that in the other geological layers. It can be seenin FIG. 6A that the injection of carbon dioxide for 10 years has openeda fracture in the caprock and leaked pressurized carbon dioxide into theoverburden layers. The pore pressure attained higher values at the pointof leakage in the overburden layers, and therefore, influences the porepressure buildup. In the case of non-fractured caprock shown in FIG. 6B,the injection increased the pore pressure mainly in the injectionreservoir. It can be seen that the pressure buildup is relatively lowerin the fractured caprock, because of the leakage of the pressurizedcarbon dioxide into the overburden layers. This leakage results in anincrease of the local pore pressure.

The pore pressure increase due to injection for the 10-year period isshown in FIG. 7A, 7B. The injection pressure was varied in the range of23-27 MPa for both fractured (FIG. 7A) and non-fractured cases (FIG.7B). As shown in FIG. 7A, 7B, the carbon dioxide injection pressure hasa considerable effect on the pore pressure buildup in the reservoir. Forexample, at 1500 days, the pore pressure in the fractured well of FIG.7A is about 20K kPa. For the same term, the pore pressure in thenon-fractured well of FIG. 7B is about 21K kPa, as the CO₂ has notleaked. The magnitude of pore pressure increases with an increase in thevalue of the injection pressure. The spread of carbon dioxide in thereservoir is dependent on the pressure difference between the injectedcarbon dioxide and reservoir pressure. It is therefore recommended tofirst calculate the maximum possible safe value for the injectionpressure for the reservoir before starting injection.

The pore pressure buildup in the reservoir at an injection pressure of27 MPa is shown in FIG. 8 for both fractured (solid line) andnon-fractured caprocks (dotted line). The pore pressure build up isabout 1000 kPa higher for the non-fractured caprock than for thefractured caprock, indication that the non-fractured caprock is notleaking CO₂.

For non-fractured caprock, the pressure response of the reservoir isshown in FIGS. 9A-C and FIG. 10. FIG. 9A illustrates the reservoirpressure response from CO₂ injection after 2 years. FIG. 9B shows thereservoir pressure response from CO₂ injection after 6 years and FIG. 9Cillustrates the reservoir pressure response from CO₂ injection after 10years. FIG. 10 is a graph showing the reservoir pressure response atvarious injection pressures during CO₂ injection. The pressure responseobtained using the COMSOL multiphysics software was in good agreementwith the results of the CMG-GEM software, for the same injection andreservoir parameters.

The effect of the location of the fracture zone in the caprock on thepore pressure in the overburden layers was determined. The magnitude ofthe pore pressure in the Wasia overburden layer above the caprock isshown in FIG. 11A, B, C for a fractured zone at the distances of 200(FIG. 11A), 400 (FIG. 11B), and 600 m (FIG. 11C) from the injectionwell. As the carbon dioxide starts spreading in the reservoir, thereservoir pore pressure starts to increase, with its distribution havinga maximum value near the injection point 1120. The highly pressurizedcarbon dioxide will leak first into fractures that are closer to theinjection point. The leaked highly pressurized carbon dioxide results inpore pressure buildup in the overburden layers. It can be observed thatthe magnitude of the pore pressure reaches relatively higher values asthe fractured zone gets closer to the injection well.

The methods of the present disclosure predict ground uplift during CO₂injection as described below.

The increase in the pore pressure results in the deformation of thereservoir, thus causing vertical ground uplift. The vertical grounddisplacement can be calculated from the geo-mechanical module in theCMG-GEM. For both cases of the fractured and non-fractured caprocks, thevertical ground displacement was calculated for the 10-year injectionperiod at different injection pressures. In FIG. 12A, it can be seenthat for the case of the non-fractured caprock, the ground verticaldisplacement attains higher values just above the injection point at thecenter of the reservoir. However, it is interesting to note that, forthe case of fractured caprock, shown in FIG. 12B, the ground verticaldisplacement is centered above the fractured zone. In the case of thefractured caprock, as the pressurized carbon dioxide is leaked into theoverburden layers, their volumetric expansion becomes higher at thepoint of leakage, which causes the ground vertical displacement to behigher above this point. It is important to state that the increase inthe ground vertical displacement just above the fractured zone helps inidentifying the location of the fractured zone in the caprock. Theincrease in the pore pressure gives rise to higher values of the grounduplift, as depicted in FIG. 13A, 13B. FIG. 13A illustrates groundvertical displacement during CO2 injection for the 10-year injectionperiod at different injection pressures in fractured caprock and FIG.13B illustrates ground vertical displacement during CO2 injection forthe 10-year injection period at different injection pressures innon-fractured caprock. The excessive ground uplift can cause damage tothe surrounding infrastructure, and any carbon dioxide leakage mayaffect environmental air quality.

Permeability measures the ability of fluids to flow through rock (orother porous media). A Darcy is a permeability unit which is widely usedin petroleum engineering and geology and has dimensional units oflength. A medium with a permeability of 1 Darcy permits a flow of 1cm³/s of a fluid with viscosity 1 cP (1 mPa·s) under a pressure gradientof 1 atm/cm acting across an area of 1 cm². Typical values ofpermeability range as high as 100,000 Darcys for gravel, to less than0.01 microDarcy for granite. Sand has a permeability of approximately 1Darcy. The Darcy is defined using Darcy's law, which can be written as:

$\begin{matrix}{Q = \frac{{Ak}\;\Delta\; P}{\mu\;\Delta\; x}} & (16)\end{matrix}$

where:

-   -   Q is the volumetric fluid flow rough the medium:    -   A is the area of the medium    -   k is the permeability of the medium    -   μ is the: dynamic viscosity of the fluid    -   ΔP is the applied pressure difference    -   Δx is the thickness of the medium

There is a relationship between fractured zone permeability and theamount of carbon dioxide leakage to the overburden layers andconsequently on the vertical ground uplift. To evaluate the effect offracture permeability on the vertical ground displacement, a fracturezone in the caprock at 200 m was considered. The influence of fracturedzone permeability on the vertical ground uplift is shown in FIG.14A-14D, in which the vertical ground displacement above the fracturedzone decreases as the permeability of the fractured zone is decreased.This is shown in FIG. 14A for 1 milliDarcy, in FIG. 14B for 25milliDarcy, in FIG. 14C for 50 milliDarcy, and in FIG. 14D for 100milliDarcy.

At lower values of the permeability, less carbon dioxide leaks to theoverburden layers and subsequently less pore pressure in the overburdenlayers. The lower pore pressure buildup corresponds to a smallermagnitude of ground uplift above the leakage point. Accordingly, thepermeability of the reservoir and the initial permeability of thefracture zone should be considered before carbon dioxide is injected. Ifthe permeability of the fractured zone is high, it is recommended toselect another suitable location for injection, either with no fracturedzone or with a fractured zone of low permeability. Furthermore, one mustexamine the effect of the fracture zone location in the caprock on thevertical ground displacement. FIG. 15A-15C display the vertical grounddisplacement for a fractured zone located at 200 m (FIG. 15A), 400 m(FIG. 15B), and 600 m (FIG. 15C), sequentially from the injection well.It can be noted that the fracture zone spread is greater for a fracturezone at 200 m from the injection well as shown in FIG. 15A, than it isin either FIG. 15B or FIG. 15C. Additionally, the fracture zone spreadis greater for the fracture at 400 m than it is at 600 m as shown bycomparing FIG. 15B and FIG. 15C respectively. This result verifies thatthe magnitude of the pore pressure is higher when the fractured zone iscloser to the injection well. Therefore, when injecting carbon dioxideinto a fractured reservoir, it should be ascertained that the increasein the pore pressure and the decrease in the effective stresses do notopen the fracture and cause carbon dioxide to leak through theoverburden layers to the atmosphere, in order to prevent the storedcarbon dioxide from entering potable water layers. For the case ofnon-fractured caprock, the ground uplift is shown in FIG. 16 atdifferent injection pressures over a 10-year period. It is clear fromthe graph that the ground uplift after 1500 days is about 15 mm at 23MPa injection pressure, (dashed line), about 16.5 mm at 25 MPa injectionpressure (dotted line) and about 18 mm at 27 MPa injection pressure(solid line). The ground uplift obtained using COMSOL was found to be ingood agreement with the ground uplift calculated by the CMG-GEM softwarefor the same injection and reservoir parameters.

The model further incorporates a coupled stability analysis of thereservoir. In order to model the carbon dioxide injection into theBiyadh reservoir, the two-phase flow and geo-mechanical analyses areused to calculate the corresponding deformation of the reservoir. Asshown in FIG. 6B, the pore pressure buildup assumes higher values in thecase of the non-fractured caprock. The increase in the pore pressure isknown to decreasethe effective stresses, which may lead to the failureof the reservoir structure if the pore pressure reaches a criticalvalue. (See Streit J E, Hillis R R (2004) “Estimating fault stabilityand sustainable fluid pressures for underground storage of CO₂ in porousrock”. Energy 29:1445-1456; Jtirgen ES, Siggins F A, Brian J E (2005)“Predicting and monitoring geo-mechanical effects of CO₂ injection.Carbon dioxide capture for storage in deep geologic formations”.2:751-766; Papanastasiou P, Thiercelin M (2011) “Modeling boreholeperforation collapse with the capability of predicting the scaleeffect”. Int J Geomech:286-293.https://doi.org/10.1061/(ASCE)GM.1943-5622.0000013; and Poon-Hwei C(1992) “Stability analysis in geomechanics by linear programming. I:Formulation”. Int J Geotech Geo Environ Eng.https://doi.org/10.1061/(ASCE)0733-9410(1992)118:11(1696), eachincorporated herein by reference in their entirety). However, in thecase of fractured caprock, the pressurized carbon dioxide leaks into theoverburden layers, thus decreasing the pore pressure.

The Mohr-Coulomb failure criterion has been utilized to perform thecoupled stability analysis of the reservoir during injection. As shownin FIG. 7A, 7B, the maximum pressure buildup in the reservoir wasrecorded at the injection pressure of 27 MPa. The stability analysis wasperformed using both CMG-GEM and COMSOL multiphysics software. Thefailure envelope of Biyadh reservoir is shown in FIG. 17A fracturedcaprock and in FIG. 17B for non-fractured caprock structures. The dottedcircle in FIG. 17A, 17B shows the initial stressed conditions based onthe following: the initial pore pressure of 11.9 MPa, the minimumprinciple stress of 29.63 MPa, and the maximum principle stress of 37.04MPa. After 10 years of injection, the final stressed condition shown inFIG. 17A, 17B indicates that the pressure buildup in the case offractured caprock is not high enough to cause failure of the reservoir.This is attributed to carbon dioxide leakage into the overburden layers,which limits the pressure buildup. Even for high values of pressurebuildup in the case of non-fractured caprock, the reservoir is stillsafe for the 10-year injection period. As shown in FIG. 17A, 17B, thestability analyses performed using the CMG-GEM and COMSOL are in goodagreement. Any further injection of carbon dioxide may cause excessivepore pressure buildup and may cause the failure of the reservoir.

In an aspect of the present disclosure, a numerical modeling scheme wasdeveloped to simulate carbon dioxide injection into the Biyadh sandstonereservoir. The coupled geo-mechanical analysis was performed using boththe CMG-GEM and COMSOL software to evaluate the feasibility of using theBiyadh reservoir for carbon dioxide sequestration. Caprock lifting forthe Biyadh reservoir is analyzed and compared for the cases of having nofractures and having fractures.

Large-scale injection of carbon dioxide is a highly sensitive processthat needs a continuous monitoring of the stored gas. If only a smallamount of carbon dioxide is leaked from the reservoir, it can haveadverse effects on the environment and may jeopardize the safety ofresidents in the vicinity of the sequestration site. It is thereforehighly recommended to model the possible leakage of carbon dioxide fromthe reservoir in order to estimate the safe values of the injectionparameters and safe storage capacity for the injection reservoir.

CO₂ sequestration in a naturally fractured carbonate reservoir wasmodelled numerically. In this context, the COMSOL multi-physics softwarewas employed with equation-based modelling using the Warren and Rootfracture model for the fractured medium. (See Warren, J. E. and Root, P.J. (1963) “The behavior of naturally fractured reservoirs”, Soc. Pet.Eng. J., Vol. 3, No. 3, pp. 245-255, incorporated herein by reference inits entirety).

The governing equations of the finite element model are described below,including the sorption effects. Additionally, the method for modellingmultiple injection wells is described.

The governing equations consider the fracture system as pathways betweenmatrix elements. Carbon dioxide flows through the fractures and is thenadsorbed in the matrix. The coupled field equation of the carbon dioxideflow and the reservoir deformations is:

$\begin{matrix}{{{Gu}_{i,{kk}} + {\frac{G}{1 - {2v}}u_{k,{ki}}} - {\alpha\; p_{m,i}} - {\beta\; p_{f,i}} - {K\;\frac{ɛ_{{Lp}_{L}}}{\left( {p_{m} + p_{L}} \right)^{2}}p_{m,i}} + f_{i}} = 0} & (17)\end{matrix}$where G is the shear modulus, u represents the displacement vector, v isthe Poisson's ratio, α and β are the Biot coefficients for matrix andfractures respectively. P_(m) and P_(f) are the pressures in the matrixand fractures of the reservoir. K is the bulk modulus for the reservoir,ε_(L) is the Langmuir volumetric strain constant, P_(L) is the Langmuirpressure constant, f_(i) represents the body force.

The displacement field of the reservoir is dependent on CO₂injection-induced pore pressure changes in the matrix and fractures.Accordingly, the flow of carbon dioxide along the naturally fracturedmedium can be represented by:

$\begin{matrix}{{{\left\lbrack {\varnothing_{m} + {\rho_{ga}\rho_{c}\frac{v_{L}p_{L}}{\left( {{pm} + {pL}} \right)^{2}}} + \frac{\left( {\alpha - \varnothing_{m}} \right){pm}}{\left( {1 + S} \right)K_{s}} - \frac{\left( {\alpha - \varnothing_{m}} \right)p_{L}{pm}\; ɛ_{L}}{\left( {1 + S} \right)\left( {{pm} + {pL}} \right)^{2}}} \right\rbrack\frac{\partial p_{m}}{\partial t}} + {\nabla{\cdot \left( {{- \frac{k_{m}}{\mu}}p_{m}{\nabla{\cdot p_{m}}}} \right)}}} = {{\omega\left( {p_{f} - p_{m}} \right)} - {\frac{\left( {\alpha - \varnothing_{m}} \right){pm}}{\left( {1 + S} \right)}\frac{\partial e_{v}}{\partial t}}}} & (18) \\{{{{\varnothing_{f}\left( {1 + \frac{{pf}\;\beta}{K_{n}}} \right)}\frac{\partial p_{f}}{\partial t}} - {{\varnothing_{f}\left( {\frac{{pf}\;\alpha}{K_{s}} + \frac{p_{L}{pm}\; ɛ_{L}}{\left( {{pm} + {pL}} \right)^{2}}} \right)}\frac{\partial p_{m}}{\partial t}} + {\nabla{\cdot \left( {{- \frac{k_{f}}{\mu}}{p_{f} \cdot {\nabla{\cdot p_{f}}}}} \right)}}} = {{- {\omega\left( {p_{f} - p_{m}} \right)}} - {p_{f}{\varnothing_{f}\left( {\frac{1}{K_{n}} - \frac{1}{K_{s}}} \right)}\frac{\partial\left( \frac{\sigma_{kk}}{3} \right)}{\partial t}}}} & (19)\end{matrix}$where Ø_(m) is the porosity of the matrix, Ø_(f) is the porosity of thefractures, V_(L) is the Langmuir volume constant, ω is a coefficientthat takes into account the flow between fractures and matrix, ρ_(c) isthe density of the reservoir rock, ρ_(ga) is the density of carbondioxide at standard conditions, and S is defined as

$\begin{matrix}{S = {ɛ_{v} + \frac{p_{m}}{K_{s}} - ɛ_{s}}} & (20)\end{matrix}$where ε_(v) and ε_(s) are volumetric and sorption induced strains,respectively. K_(s) is the grain elastic modulus, K_(n) is the normalstiffness of the fractures, k_(m) and k_(f) are the matrix and fracturespermeability respectively, and μ is the viscosity of the carbon dioxide.It is important to note that the change in the pore pressure causes achange in the value of volumetric strain that will eventually result invertical ground uplift with the passage of time as carbon dioxide isinjected.

COMSOL multiphysics software was used to model the reservoir and theoverburden layers between the ground surface and the reservoir. Thestep-by-step process of the model construction including variousconstraints, in addition to initial and boundary conditions arediscussed below.

Starting with the Arab Jubaila carbonate reservoir 110 shown in FIG. 1,each geological layer was modelled in COMSOL, such that each layer has adifferent thickness value. Starting with a single injection well, thenumber of injection wells was increased up to four. A non-limitingexample of the modelling of the Ghawar Arab-D carbonate reservoir withdifferent arrangements of injection wells is shown in FIG. 18A-18D. FIG.18A shows CO₂ injection in a single well, FIG. 18B shows CO₂ injectionin two wells, FIG. 18C depicts the injection into three wells in atriangular pattern and FIG. 18D depicts the injection into four wells ina rectangular pattern.

Each of the models in FIG. 18A-18D has a total of 276,660 degrees offreedom with five independent variables at each node (two pressures andthree displacement components). The two pressure variables are for thematrix pore pressure and the fracture pressure. For calculation ofground vertical uplift due to carbon dioxide injection, the bottomsurface of each simulation model is constrained, the surfaces defined bynormal along x and y axes are described by roller boundary conditions,and the top surfaces are left free for each of the simulation models.The formation properties and various input parameters are listed inTable 3. The overall simulation properties for CO₂ injection scenariosinto the multi-layer 3D models for the Ghawar location is given in Table4.

TABLE 3 Formation properties for the simulation of CO2 injection into acarbonate reservoir. For For For under Model parameter reservoir caprockburden layer Rock density, 2400 1870 2550 ρ (Kg/m³) Young's modulus,48.5 37.05 53.5 E (GPa) Bulk modulus, 39.24 23.75 34.5 K (GPa) Shearmodulus, 18.1 13.8 19 9 G (GPa) Initial porosity, ∅_(m) 0.13 0.01 0.10Initial permeability, 0.6 0.00001 0.2 k_(m) (10⁻¹⁵ m²) Biot coefficient,α 0.8 0.2 0.4 Dynamic viscosity, 1.84 1.84 1.84 μ (10⁻⁵ Pa · s) Pressurewave 5140 4750 4900 velocity Vp (m/sec) Shear wave 2748 2770 7800velocity, Vs (msec)

TABLE 4 Overall simulation properties for CO2 injection into the Ghawarcarbonate reservoir. CO₂ injection rate 1,000 (31.71 (kTons/year)kg/sec) CO₂ injection 5 period (years) Overall model 3,000 × dimensions,length × 2,000 × 2,170 width × height (m)

The Ghawar oil field is undergoing a compressional stress regimeaccording to the World Stress Map, which tends to produce compressivestresses in the reservoir structure. The World Stress Map (WSM) is aglobal compilation of information on the crustal present-day stressfield maintained since 2009 at the Helmholtz Centre Potsdam GFZ GermanResearch Centre for Geosciences within Section 2.6 Seismic Hazard andStress Field. This is a collaborative project between academia andindustry which aims to characterize crustal stress patterns andunderstand the stress sources. (See Abdulkader, M. A. (2005) “Ghawar:The Anatomy of the World's Largest Oil Field”, Saudi Aramco Search andDiscovery, Article#20026, Saudi Arabia; and World Stress Map (2008)[online] http://dc-app3-14.gfzpotsdam.de/pub/poster/World_Stress_Map_Release_2008.pdf (accessed 20June 2015), each incorporated herein by reference in their entirety).The pre-stresses on the sedimentary reservoirs are due to the weight ofthe overburden layers in the vertical direction, and due to the tectoniceffects along the two horizontal directions. For the compressionalstress regime, the relationship between the magnitudes of the threeprincipal stresses is such that, ρ₁>σ₂>σ₃, where σ₁ is equal to themaximum horizontal stress (σ_(H)), σ₂ is the minimum horizontal stress,and σ₃ represents the vertical stress caused by the weight of theoverburden layers. (See Byerlee, J. (1978) “Friction of rocks”, Pure andApplied Geophysics, Vol. 116, No. 1, pp. 615-626; Hergert, T. andHeidbach, O. (2011) “Geomechanical model of the Marmara Sea region-II.3-D contemporary background stress field”, Geophysical JournalInternational, Vol. 3, No. 3, pp. 1090-1120; and Rutqvist, J.,Birkholzer, J. T., Cappa, F. and Tsang, C. (2007) “Estimating maximumsustainable injection pressure during geological sequestration of CO₂using coupled fluid flow and geo-mechanical fault-slip analysis”, EnergyConversion and Management, Vol. 48, No. 6, pp. 1798-1807, eachincorporated herein by reference in their entirety).

The reservoir stability analysis using Mohr-Coulomb criterion ispresented below. The flow and transport of carbon dioxide along thereservoir is strongly dependent on the injection pressure. The more theinjection pressure increases, the more the flow of carbon dioxideincreases into the reservoir. For maximum storage capacity of carbondioxide, it is desirable to increase the injection pressure. However, itis necessary to observe the estimated safe values of the injectionpressure. The safe values of the injection pressure are obviously lessthan the critical pore pressures. The modelling of one injection wellwas extended to include multiple injection wells. The pore pressurevariations for various arrangements of injection wells were determined.The resulting ground surface vertical uplift, reservoir stability andmaximum occupancy for various arrangements of injection wells were alsodetermined.

A single-well injection simulation was carried out for a five-yearinjection period. The pressure variations for different injectionperiods are displayed in FIG. 19A-19D, in which the pore pressure isshown to increase with carbon dioxide injection. The region of thereservoir closer to the injection well attains higher pressure ascompared to the regions far away from the well. The vertical grounduplift after a five-year injection period was found to have a maximumvalue of 17.1 mm as shown in FIG. 20. As shown in the contour map on thetop surface of FIG. 20, the injection of carbon dioxide for a period offive years causes the vertical uplift of the ground above and around theinjection well. The value of the ground vertical uplift has a maximumvalue above the injection well and is extended for several kilometersaround the injection well.

The Mohr-Coulomb failure criterion for the compressional stress regimewas used to analyze the effect of pore pressure variation on thereservoir stability. Both increases and decreases in the pore pressurecan cause failure of the reservoir due to the subsequent changes in themagnitude of effective stresses in the reservoir. (See Jtirgen, E. S.,Siggins, F. A. and Brian, J. E. (2005) “Predicting and monitoringgeo-mechanical effects of CO₂ injection”, Greenhouse gas controltechnologies: Proceedings of the 7th International Conference onGreenhouse Gas Control Technologies, Oxford, Elsevier, Vol. 1; andStreit, J. E. and Hillis, R. R. (2004) “Estimating fault stability andsustainable fluid pressures for underground storage of CO₂ in porousrock”, Energy, Vol. 29, No. 9, pp. 1445-1456, each incorporated hereinby reference in their entirety). The Mohr-Coulomb failure criterion isutilized to draw the failure envelope for the reservoir. It is assumedthat the reservoir is of an intact rock type due to the fact that nomajor fault passes through the reservoir. As the pore pressureincreases, the effective stress on the reservoir decreases and thereservoir tends to move to a new stress condition that is nearer to thefailure line as compared to the initial stress condition. The stabilityanalysis also takes into account the change in the horizontal stressesdue to the pore pressure which has built up. For one injection well, thepore pressure increases to a maximum of 25.8 MPa from an initial porepressure of 11 MPa at the reservoir. The effect of pore pressureincrease in the compressional stress regime is different from otherstress regimes. As the pore pressure is increases, the horizontalstresses in the reservoir increase due to the coupled poro-elasticeffects. With one injection well and with the carbon dioxide injectionscenario given in Table 4, injection within the reservoir remains atsafe levels.

For the non-limiting example of the Arab Jubaila reservoir, the initialpore volume calculated from the reservoir is 1.6926×10⁹ m³. For theinjection parameters given in Table 4, the volume of carbon dioxide atthe ground level is equal to 2.5252×10⁹ m³ after five years ofinjection. At the reservoir's depth, the carbon dioxide exists in adense state with comparatively less volume than that at the groundlevel. At a reservoir depth of 1,750 meters, the formation volume factorfor the reservoir is 0.00275 m³/m³, which corresponds to 6.94×10⁶ m³ ofcarbon dioxide injection volume, with occupancy of 0.41% of theavailable pore volume. (See Hassan, Z. H., Mehran, P. D., Elsharkawy, A.M., David, W. K. and Leonenko, Y. (2008) “Predicting PVT data forCO₂-brine mixtures for black-oil simulation of CO₂ geological storage”,International Journal of Green House Gas Control, Vol. 2, No. 1, pp.65-77, incorporated herein by reference in its entirety). The maximumoccupancy value for a closed boundary reservoir is 2 to 3% of the totalavailable volume which shows that the current injection scenario withone injection well is within the safe limit.

In the case of two injection wells, the wells are arranged in-line, i.e.the injection wells are placed along a line along the length of thereservoir which passes through the center of the reservoir. Withsymmetric placement of the injection wells along the center line of thewells, the various arrangements of the injection wells are given inTable 5.

TABLE 5 Different in-line two well arrangements. Central Arrangementspacing (m) Case 1   600 Case 2   800 Case 3 1,000 Case 4 1,200

The numerical simulation results for the two injection wells spaced at600, 800, 1,000, and 1,200 meters are depicted in FIG. 21A-21 d and FIG.22A-22D. The pressure variation after a five-year injection period isshown in FIG. 21A-21D. The injection wells spaced apart by 800 meters(FIG. 21A) have the lowest pore pressure build-up, while the injectionwells spaced apart at 1,200 meters yield the maximum pressure build-upvalue (FIG. 21D).

The vertical ground uplift after five years of injection period is shownin FIG. 22A-22D. Two wells at 600 meters (FIG. 22A) distance results ina maximum vertical ground uplift of 24.4 mm, two wells at 800 meters(FIG. 22B) distance yield a maximum vertical uplift of 23.1 mm, twowells at 1,000 meters (FIG. 22C) distance result in a maximum verticaluplift of 24.8 mm, and two wells at 1,200 meters (FIG. 22C) distanceyield a maximum vertical uplift of 25.1 mm. The increase in the porepressure for the case of two-well injection, spaced centrally at 1,200meters, is higher than that of a single-well injection. The new stressedcondition of the reservoir is closer to the failure line, as compared tothe case of a single-injection well. Yet, for the two-well injectionscenarios considered in Table 5, the reservoir remains within a safe andstable limits.

For an initial volume of 1.6926×10⁹ m³ for the reservoir, the volume ofcarbon dioxide injected during the five-year injection period is5.0504×10⁹ m³ at ground level. Due to the high pressure at the reservoirdepth of 1,750 meters, the volume of the carbon dioxide will decreasewith a factor of 0.00275 m³. Accordingly, the volume of carbon dioxideat the reservoir level is 13.88×10⁶ m³, which is about 0.82% of theavailable pore volume. At a maximum occupancy limit of (2% to 3%) of thetotal available volume, the current two-well injection scenario iswithin the safe limits.

For three-well injection, the different patterns in which carbon dioxideinjection was simulated is given in Table 6. In the case of three wells,the different well arrangements are in-line and central (equally spacedaround the center of the well). The selection of an optimum wellarrangement depends on the dimensions of the reservoir. After observingthe pore pressure increase for various cases of three-well injection,the conclusion was drawn that, for a reservoir with minimum width andthickness as compared to its length, in-line well arrangements are moresuccessful than the central wells arrangements. However, if the width ofthe reservoir has almost equal value to the length of the reservoir,then the optimum central well arrangements can keep the pore pressurevalue much less than the critical pore pressure for the reservoir. Themaximum pore pressure for each pattern of three-well injection and itscorresponding effect on reservoir stability is explained in thefollowing sections.

TABLE 6 Different three well injection arrangements. Arrangement Centralspacing (m) Case 1 Equilateral triangular arrangement; l = 300 m Case 2Equilateral triangular arrangement; l = 400 m Case 3 Equilateraltriangular arrangement; l = 500 m Case 4 Equilateral triangulararrangement; l = 600 m Case 5 In-line arrangement; l = 500 m Case 6In-line arrangement; l = 600 m Case 7 In-line arrangement; l = 700 mCase 8 In-line arrangement; l = 800 m

The following section summarizes the numerical simulation results forthe various arrangements of three-well injection arrangements given inTable 6. After a five-year injection period, the pressure variations areshown in FIG. 23A-23H, wherein the pore pressure is shown to increasewith carbon dioxide injection. FIG. 23A shows the pressure increaseafter five years for an equilateral triangular arrangement of injectionwells spaced at 300 m apart increasing from 2.8×10⁷ to 3.2×10⁷ MPa. FIG.23B depicts injection wells spaced at 400 m for an equilateraltriangular arrangement of injection wells with pressure increasing to3.16×10⁷ MPa, FIG. 23C depicts injection wells spaced at 500 m inequilateral triangular arrangement with pressure increasing to 3.2×10⁷MPa, FIG. 23D depicts injection wells spaced at 600 m in equilateraltriangular arrangement with pressure increasing to 3.23×10⁷ MPa, FIG.23E depicts injection wells spaced at 500 m in an in-line arrangementwith pressure increasing to 3.18×10⁷ MPa, FIG. 23F depicts injectionwells spaced at 600 m in an in-line arrangement , with pressureincreasing to 3.11×10⁷ MPa, FIG. 23G depicts injection wells spaced at700 m in an in-line arrangement with pressure increasing to 3.15×10⁷ MPaand FIG. 23H depicts injection wells spaced at 800 m in an in-linearrangement with pressure increasing to 3.17×10⁷ MPa.

The vertical ground uplift after a five year injection period is shownin FIG. 24A-24H. Three wells at 300 meters distance from reservoircenter show a maximum vertical ground uplift of 28.1 mm (FIG. 24A),three wells at 400 meters distance from reservoir center show maximumvertical ground uplift of 27.3 mm (FIG. 24B), three wells at 500 metersdistance from reservoir center show maximum vertical ground uplift of27.8 mm (FIG. 24C), and three wells at 600 meters distance fromreservoir center show maximum vertical ground uplift of 28.2 mm (FIG.24D). Similarly, three wells with in-line arrangement at a distance of500 meters show a vertical ground uplift of 27.6 mm (FIG. 24E), threewells with inline arrangement at a distance of 600 meters show avertical ground uplift of 26.5 mm (FIG. 24F), three wells with in-linearrangement at a distance of 700 meters show a vertical ground uplift of27.3 mm (FIG. 24G), and three wells with in-line arrangement at adistance of 800 meters show a vertical ground uplift of 27.5 mm (FIG.24H).

The caprock uplift may be monitored for a period of time, and comparedto a threshold. An alarm may be provided when the caprock uplift isgreater than the threshold. The threshold may be 35 mm, preferably 25mm, more preferably 20 mm, even more preferably 15 mm, even morepreferably 10 mm or less, even more preferably 5 mm or less.

Caprock uplift may be monitored by a comparison of satellite images ofthe caprock of the reservoir over a period of time.

The period of time may be selected from the range of one to one hundredyears, preferably one to fifty years, even more preferably one to twentyfive years and even more preferably one to ten years.

Additionally, a fracture in the subsurface layers may be identified at alocation of caprock uplift. An alarming system may notify an oilfieldmanagement authority of the caprock uplift and its location. Inresponse, the injection pressures may be adjusted or an injection wellin the location of the caprock uplift may be shut down.

The pore pressure increase is more for the case of three injection wellsat 600 meters distance from the reservoir center as compared to otherthree wells arrangements. With three injection wells at 600 meters fromthe reservoir center, the reservoir is more nearer to the failureenvelope as compared to the cases of single and two injection wells.However, the reservoir maintains the safe stable condition. A. at 300 mtriangular B. at 400 m triangular C. at 500 m triangular D. at 600 mtriangular E. at 500 m in-line F. at 600 m in-line G.at 700 m in-line H.at 800 m in-line.

With three injection wells the volume of carbon dioxide injected intothe reservoir at the ground level is equal to 7.5756×10⁹ m³ for fiveyears of injection period. Due to the high pressure value of thereservoir, the volume of the injected carbon dioxide decreases to20.83×10⁶ m³, which is 1.23% of the available pore volume of thereservoir. Still with an occupancy of 1.23%, the reservoir will be onsafe side because this occupancy value is less than 2% to 3%. 2% to 3%of the available reservoir pore volume is the maximum occupancy limit.

The different patterns for the four well injection scenario are given inTable 7. In the case of four injection wells, different wellarrangements that are equally spaced away from the center of the wellare considered. In the first three cases tabulated in Table 7, the fourwells are arranged in the form of a square, with the center of thesquare coincident with the reservoir's center. In the last case in Table7, the four injection wells are arranged in the form of a rectangle,with its center being coincident with the reservoir center. The porepressure variation for each pattern and its corresponding effect on thereservoir's stability are explained in the following sections.

TABLE 7 Four well injection arrangements Different cases for four-wellinjection Central spacing (m) Case 1 Square arrangement with each of thefour wells spaced at a distance of 400 m from the reservoir centre. Case2 Square arrangement with each of the four wells spaced at a distance of500 m from the reservoir centre. Case 3 Square arrangement with each ofthe four wells spaced at a distance of 600 m from the reservoir centre.Case 4 Rectangular arrangement with each of the four wells spaced at adistance of 700 m from the reservoir centre at a diagonal angle of34.85° with line passing through the reservoir centre along the lengthof the reservoir.

The numerical simulation results for the four injection wells at 400,500, 600, and 700 meters distance from the reservoir center are shown inFIG. 25A to 25D and FIG. 26A to FIG. 26D. After a five year injectionperiod, the pressure variation is shown in FIG. 25A to 25D. For a fourwell square arrangement spaced at 400 m (FIG. 25A), the pore pressureincreased from 2.9×10⁷ MPa to 3.26×10⁷ MPa. For a four well squarearrangement spaced at 400 m (FIG. 25A) from the reservoir center, thepore pressure increased from 2.9×10⁷ MPa to 3.26×10⁷ MPa. For a fourwell square arrangement spaced at 500 m (FIG. 25B), the pore pressureincreased from 2.9×10⁷ MPa to 3.23×10⁷ MPa. For a four well squarearrangement spaced at 600 m (FIG. 25C), the pore pressure increased from2.9×10⁷ MPa to 3.27×10⁷ MPa. For a four well rectangular arrangementspaced at 700 m (FIG. 25A) at a diagonal angle of 34.85 degrees withline passing through the reservoir center, the pore pressure increasedfrom 2.9×10⁷ MPa to 3.34×10⁷ MPa.

The vertical ground uplift after five years of injection is shown inFIG. 26A-FIG. 26D. The four-well arrangements at 400, 500, 600 and 700meters from the reservoir center attained maximum values of verticalground uplift of 28.9 mm (FIG. 26A), 28.3 mm (FIG. 26B), 29.1 mm (FIG.26C) and 30.2 mm (FIG. 26D), respectively. For the four-well arrangementat 700 meters from the reservoir center, the pore pressure attained ahigher increase relative to other four-well arrangements while remainingwithin safe limits.

For the four well injection arrangements, an amount of 10.1008×10⁹ m³ ofcarbon dioxide was injected into the reservoir at ground level. At thereservoir level of 1,750 meters, the carbon dioxide is stored in a denseform at a volume of 27.77×10⁶ m³, with occupancy of 1.64% of theavailable pore volume. The maximum occupancy value for the reservoir is3% of the total available volume which demonstrates that the currentinjection scenario with four wells remains within the safe limit of2-3%.

The maximum pore pressure for various two-well injection arrangements ofTable 5 are summarized in FIG. 27A wherein cases 1 to 4 represent twoinjection wells that are spaced by a central distance of 600, 800, 1,000and 1,200 meters, respectively. The pore pressure for case 1 is higherthan that for case 2 due the interaction between the pore pressureprofiles that tends to increase the overall pore pressure value as thetwo wells become closer. However, this trend is reversed as theinjection wells get closer to the boundaries of the reservoir, as shownfor cases 3 and 4. In this case, the highest pressure build-up is forthe case of two wells spaced by at a distance of 1,200 meters at about2.95×10⁷ MPa.

The maximum pore pressure for different three-injection wellarrangements is summarized in FIG. 27B. The various cases shown in FIG.27B were explained in Table 6. Cases 1 to 4 are equilateral triangulararrangements, and cases 5 to 8 are in-line arrangements. FIG. 27B showsthat the equilateral triangular arrangements of the injection wells havehigher pore pressure build-up as compared to the in-line wellarrangements. One explanation for this equilateral triangulararrangements place the injection wells nearer to the reservoir boundarywalls as compared to the in-line well arrangements. Among theequilateral triangular arrangements, the optimum arrangement with lesspressure build-up is case 2 with three equilateral injection wells at adistance of 400 meters from the reservoir center. Among the in-linewells arrangements the optimum arrangement with less pressure build-upis case 6 with three injection wells placed in-line such that one of thewell is at the reservoir center and the other two are at a distance of600 meters from the central well.

FIG. 27C shows the maximum pore pressure for different four-wellinjection arrangements listed in Table 7. Among the four cases, theminimum pore pressure build-up was found for case 2 at 500 meter spacingabout 32.3×10⁷ MPa, while the maximum pressure build-up was for case 4at 700 meter spacing from the reservoir center was 33.4×10⁷ MPa. In case4, the value of the pore pressure after carbon dioxide injection ishigher due to the reason that the injection wells are much closer to theboundary walls of the reservoir, which stop the flow of CO₂.

The above detailed aspects of the present disclosure, illustrated inFIG. 18A to 27C, determined the effect on reducing the pore pressurebuild-up and increasing the reservoir storage capacity by varying boththe number and arrangement of carbon dioxide injection wells. Theequation-based modelling technique in COMSOL multi- physics finiteelement software was utilized for the numerical modelling of differentcarbon dioxide injection scenarios.

The effect of the reservoir size and boundary conditions selection areinvestigated using geo-mechanical modeling of a reservoir undergoingcarbon dioxide injection. This investigation determines relationshipsbetween reservoir size and boundary conditions selection to reservoirpore pressure buildup, ground uplift, fault reactivation and reservoir'sstability. Coupled geo-mechanical modeling was performed for differentsizes of reservoir models in COMSOL multiphysics software at differentboundary conditions. The CMG-GEM (Computer Modeling GroupLtd-Geomechanical Modeling Software) was utilized to model faultreactivation during carbon dioxide injection into small and large sizereservoirs with closed boundary condition. The geo-mechanical modelingfor carbon dioxide injection was performed for carbon dioxide injectionvia single injection well at the center of the reservoir, as well as forinjection via multiple injection wells. The reservoir stability analysiswas performed using the Mohr-Coulomb failure criterion for both smalland large models at different boundary conditions.

Hydro-mechanical coupled geo-mechanical modeling was performed forcarbon dioxide injection into small and large models of a sandstonereservoir. In a non-limiting example, the sandstone reservoir is theBiyadh reservoir. During the coupled geo-mechanical modeling, the flowof carbon dioxide caused the deformation of the reservoir structure. Themodel is based on the following assumptions and simplifications:

(1) Conditions are isothermal.

(2) The simplified layered model incorporates initial values from knowndata sources and average values are used to represent the thickness ofthe various layers in the system.

(3) Geochemical modeling was not performed.

(4) A linear variation of the initial pore pressure and stresses alongthe depth is adopted.

(5) A constant value was assigned to the Biot's coefficient and auniform porosity distribution is assumed along the reservoir.

In order to model the flow of carbon dioxide in the reservoir and thecorresponding reservoir deformation due to carbon dioxide injection, twosets of governing equations were used.

The flow of carbon dioxide in the reservoir was modeled using the massconservation and Darcy's equations, as given by equation (1) and (2)respectively

$\begin{matrix}{{{\frac{\partial}{\partial t}\left( {\rho_{f}\phi} \right)} + {\nabla{\cdot \left( {\rho_{f}q} \right)}}} = Q_{m}} & (21) \\{q = {{- \frac{k}{\mu}}\left( {{\nabla\; p_{f}} + {\rho_{f}g\;{\nabla\; D}}} \right)}} & (22)\end{matrix}$

where:

ρ_(f)=density of carbon dioxide (kg/m³),

q=Darcy's velocity vector (m/sect),

p_(f)=pore pressure (Pa),

Q_(m)=source term (kg/m³),

ϕ=matrix porosity,

D=depth in the gravity direction (m),

k=permeability (mDarcy),

μ=fluid viscosity (Pa-sec).

Reservoir Deformation Equations

The deformation of the reservoir due to carbon dioxide injection wasmodeled using the reservoir stress equilibrium, stress-strain, andstrain-displacement equations as follows:−∇·σ=F _(v)=ρ_(avg) g   (23)σ−σ₀ =C:(ε−ε₀−∈_(inel))−αp _(f) I   (24)ε=½((∇u)^(T) +∇u)   (25)where:

σ=Stress tensor (N/m²),

F_(v)=Volume force vector (N/m³),

ε=strain tensor,

C=elastic tensor,

α=Biot's coefficient,

u=displacement components (in meters).

Equations (21-24) were solved for three displacement components along x,y, and z axes, in addition to the pore pressure. During carbon dioxideinjection, Darcy flow was considered in the porous medium. During themodeling procedure, the carbon dioxide flow and reservoir deformationequations were fully coupled. As implied by equation (23), the change inthe pore pressure was shown to influence the stress-strain relation andhence the displacement field in the porous medium. However, asmanifested by equation (21), the spread of carbon dioxide in thereservoir was dependent on the change in the pore pressure, thepermeability of the porous medium, and the viscosity of carbon dioxide.

The injection of carbon dioxide changes the magnitude of the effectivestresses in the reservoir. Any pre-existing fault can be activated ifthe magnitude of the effective stresses acting on the fault decreasesfrom a critical limit. The Barton-Bandis model present in CMG-GEM wasutilized to model the fault reactivation during carbon dioxide injectioninto the reservoir. The main objective of performing the faultreactivation modeling is to evaluate the effects of reservoir size andboundary conditions on fault reactivation in the reservoir. According toBarton-Bandis model, the decrease in the effective stresses due tocarbon dioxide injection will cause a significant increase in the faultpermeability and thus will cause the leakage of the trapped carbondioxide from the reservoir. In this model, a fault was inserted into theShuaiba caprock layer 122 (See FIG. 1) which is closed before carbondioxide injection. As compared to other models used in the past, theBarton-Bandis model is more efficient for modeling the faultpermeability variations during carbon dioxide injection.

The fault permeability k_(f) can be calculated as:k _(f) =k (e/e ₀)⁴   (26)where k is the fracture closure permeability, and where:

$\begin{matrix}{e = {e_{o} - V_{j}}} & (27) \\{V_{j} = \frac{\sigma_{n}}{\xi + {\sigma_{n^{\prime}}/V_{m}}}} & (28) \\{V_{m} = {e_{o}\left\lbrack {1 - \left( \frac{\lambda}{\overset{\_}{k}} \right)^{1/4}} \right\rbrack}} & (29)\end{matrix}$

The term e₀ represents the initial fracture aperture and e is thecurrent fracture aperture, V_(j) represents the fracture stiffnessratio, σ_(n′) represents the normal fracture effective stress, ξrepresents the initial normal fracture stiffness, λ represents theinitial fracture permeability, and V_(m) represents the minimum fractureaperture.

Using the non-limiting example of the Ghawar oil field, the geologicallocation of Biyadh layer 114 is seen in FIG. 1. The Biyadh sandstonereservoir is a suitable site for the long term injection of carbondioxide because: (a) it is capped by the low permeability Shuaiba layer122, and (b) it is far away from the potable water Um Er Radhuma layer124.

During the modeling procedure in COMSOL multiphysics, each layer in FIG.1 is considered to have a constant thickness in the vertical direction.

Geological maps with orientation and a scale showing the locations andages of Biyadh and Arab Jubaila reservoirs are shown in FIGS. 28 and 29.The shape of the lithology is shown in FIG. 30A-30C. FIG. 30A shows theGhawar field with five injection wells. FIG. 30B shows the lithology forthe Arab Jubaila reservoir. FIG. 30C shows the porosity and flowfractions for the zones 1, 2A, 2B, 3A, 3B and 4 of the Arab-D/Jubailalayers. In order to see the effect of reservoir size on the porepressure buildup and reservoir stability during carbon dioxideinjection, carbon dioxide was injected into both the small and largemodels, and the pressure buildup and ground uplift were compared. FIG.31A shows the small model (4000×2000) meters and FIG. 31B shows thelarge model (10,000×10,000) meters constructed in COMSOL multiphysics.

In order to see the effect of reservoir size change on pore pressurebuild-up during carbon dioxide injection using multiple injection wells,carbon dioxide was injected into reservoirs with different sizes usingtwo injection wells (116 a, 116 b). For the multiple injection wellscenarios, carbon dioxide was injected in the Arab Jubaila layer 110, asshown in FIG. 1. The different models constructed in COMSOL multiphysicsfor the case of multiple injection wells are shown in FIG. 32A-32D. FIG.32A shows an injection well of size 2800×1800 meters, FIG. 32B shows aninjection well of size 3000×2000 meters, FIG. 32C shows an injectionwell of size 6000×4000 meters and FIG. 32D shows an injection well ofsize 9000×6000 meters. The models constructed in CMG-GEM for evaluatingthe effects of reservoir size and boundary conditions on the faultreactivation are shown in FIGS. 33A and 33B. FIG. 33A depicts the smallmodel of size 4000×2000 meters and FIG. 33B depicts the large model10,000×10,000 meters.

The various parameters needed as input for modeling in COMSOLmultiphysics and CMG-GEM are listed in Table 8.

TABLE 8 Input properties of the Biyadh and Arab Jubaila reservoirs. ForFor Arab Biyadh Jubaila Model Parameter Reservoir Reservoir RockDensity. 2360 2400 ρ (Kg/m³) Young's Modulus, 44.7 48.5 E (GPa) BulkModulus, 25.7 39.24 K (GPa) Shear Modulus, 17.2 18.1 G (GPa), Initialporosity, Ø_(m) 0.12 0.13 Initial permeability, 0.7 0.9 kf (10⁻¹⁵ m²)Biot Coefficient, α 0.7 0.5 Dynamic Viscosity, 1.84 1.84 μ(10⁻⁵ Pa · s)Pressure wave 4040 2748 velocity, Vp (m/sec) Shear wave velocity, 27002748 Vs (m/sec)

During the modeling procedure, the initial values for the displacementcomponents are taken as zero, while the initial value of the porepressure is set equal to the reservoir's pressure before injection.Roller boundary condition was applied to all external boundaries, exceptthe top surface in order to allow the freedom of the ground uplift.Carbon dioxide was injected at the bottom hole surface of the well at aspecified gas entry pressure. Both the Biyadh and Arab Jubailareservoirs are under compressional stress regime, wherein the principlestresses are related such that; σ₁>σ₂>σ₃, where σ₁ and σ₂, denote themaximum and minimum horizontal stresses, respectively, and σ₃ denotesthe vertical overburden stress.

In order to avoid the error of ignoring the reservoir heterogeneity, theCOMSOL multiphysics software was coupled with MATLAB software to inputthe rock properties at each node along the reservoir. The various inputparameters shown in Table 2, Table 8 and FIG. 1 are the average values.Using the minimum and maximum values for the reservoir density, pressurewave velocity, and shear wave velocity, MATLAB functions were used tocalculate the rock properties such as modulus of elasticity, shearmodulus, modulus of rigidity, and bulk modulus.

The static modulus of elasticity is and dynamic moduli of elasticity aregiven by:E_(s) =σ/∈  (30)E _(d)=2×(1+v _(d))ρV _(s) ²   (31)

The static shear modulus (or modulus of rigidity), G_(s), and thedynamic shear modulus, G_(d), are given by:G _(s) =E _(s)/(2(1+V _(s)))   (32)G_(d)=ρV_(s) ²   (33)

The grain static modulus, K_(s), and the dynamic bulk modulus, K_(d),are given by:K _(s) =E _(s)/(3(1−2v _(s)))   (34)K _(d)=ρ(V _(p) ²−4/3V _(s) ²)   (35)

These calculated input parameters are applied to each node in the 3-dimensional injection reservoir. Other input properties such as theinitial values of rock porosity and permeability were assumed to beuniform and were taken from the literature.

In order to examine the effect of reservoir size on the pore pressurebuildup, hydro-mechanical coupled geo-mechanical modeling was performedfor carbon dioxide injection into small and large models of Biyadhsandstone reservoir. Carbon dioxide was injected at a depth of 1400meters at injection pressure in the range from 22 to 26 MPa. The maximuminjection pressure of 26 MPa used in this study is less than thelithostatic pressure for maximum reservoir stability.

With the injection of carbon dioxide into a single well reservoir, thepore pressure inside the reservoir started to increase. The porepressure buildup during carbon dioxide injection for ten years is shownin FIG. 34 (small reservoir model) and FIG. 35 (large reservoir model).As anticipated, the pore pressure increases continuously with carbondioxide injection, reaching maximum pore pressure buildup in the casewhen the small simulation model was utilized. This is due to the factthat the reservoir's boundaries in the small model are comparativelycloser to the injection port and therefore the dissipation of theinjection pressure along the reservoir is lower, thus leading to arelatively higher pore pressure buildup.

Furthermore, the variation of pore pressure during ten years of carbondioxide injection period is shown in FIG. 36 (small reservoir model) andFIG. 37 (large reservoir model), wherein the rate of pressure buildup inthe case of the large model is lower than the small model due to thefact that in large model the closed boundaries of the reservoir are faraway from the injection well which facilitates the rapid flow of carbondioxide along the reservoir. In the small model, the closed boundariesof the reservoir restrict the flow of carbon dioxide and thus the rateof pore pressure buildup.

In order to see the effect of reservoir size on pore pressure buildup inthe case of carbon dioxide injection with multiple injection wells,carbon dioxide was injected through two injection wells into reservoirsof different sizes. The two injection wells were placed in-line alongthe length of the reservoir at a distance of 600 meters from eachanother. The pore pressure buildup after carbon dioxide injection usingtwo injection wells is shown in FIG. 38A-38D. The plots in FIG. 38A-38Dshow that the reservoir size selection has a significant effect on thepore pressure buildup. FIG. 38A depicts a reservoir of 2800×1800 meterswith maximum pore pressure of 3.09×10⁷ MPa, FIG. 38B depicts a reservoirof 3000×2000 meters with maximum pore pressure of 2.93×10⁷ MPa, FIG. 38Cdepicts a reservoir of 6000×4000 meters with maximum pore pressure of2.28×10⁷ MPa and FIG. 38D depicts a reservoir of 9000×6000 meters withmaximum pore pressure of 2.14×10⁷ MPa. These results confirm that themagnitude of the pore pressure decreases as the size of the reservoir isincreased during carbon dioxide injection with multiple injection wells.These results also show that the selection of a representative volumeelement of the actual reservoir that has a size different from that ofthe actual reservoir will tend to affect the estimate of the porepressure buildup due to injection. The relatively lower pressure buildupin the case of injection into large model reservoir is due to the highpotential for the spread of carbon dioxide over the reservoir, thusdecreasing the pore pressure at any one location. The increase in thepore pressure of the smallest reservoir may be due to the effect of theboundaries that can cause pressure buildup, while the pressure buildupwill be relatively lower when the reservoir boundaries are farther away,as in the case of largest reservoir model.

In order to see the effect of boundary conditions on the pore pressurebuildup during carbon dioxide injection, different boundary conditionswere applied to both small and large reservoir models. The pore pressurebuildup in FIG. 36 and FIG. 37 during CO₂ injection for ten years waspresented for the case of the no-flow boundary condition. If carbondioxide is allowed to flow across the reservoir boundaries, themagnitude of the pore pressure buildup was shown to be different. Asshown in FIGS. 39 and 40 for open boundary conditions, the magnitude ofpore pressure after ten years of injection is less as compared to theno-flow boundary condition. The variation of the pore pressure duringthe entire ten- year injection period is shown in FIG. 39 and FIG. 40,with open boundary conditions for the small (FIG. 39) and large (FIG.40) reservoir models, respectively. It can be seen in FIG. 39 and FIG.40 that in the case of the open boundary conditions, the pore pressureincreases at a lower rate as carbon dioxide is injected into thereservoir. The effect of the injection pressure is less on the porepressure buildup in the case of reservoir with open boundary conditionsas compared to the no-flow boundary conditions. For large reservoirmodels, the effect of boundary conditions on the pore pressure buildupbecomes much less significant as compared to the small reservoir models.Table 9 compares the maximum pore pressure at 1500 days at 26 MPainjection pressure for the closed boundary conditions of FIG. 36 andFIG. 37 to the open boundary conditions of FIG. 39 and FIG. 40.

TABLE 9 Comparison of maximum pore pressure at 1500 days Maximum PorePressure (MPa) Boundary Model (approximate) Closed Small 20 Closed Large19 Open Small 18.5 Open Large 15.4

Before carbon dioxide injection into the reservoir, the reservoir has aninitial state of pore pressure and stresses. The injection of carbondioxide causes an increase in the reservoir pore pressure which causesvolumetric expansion of the reservoir structure due to its coupledgeo-mechanical behavior. During the injection process, the reservoirexpansion is allowed only in the vertical direction, while the movementof the reservoir in the lateral direction is normally restrained by theboundaries. Vertical movement of the reservoir causes ground upliftwhich needs to be monitored during the injection process. During theproduction process, the pore pressure inside the reservoir decreases andthus will cause the ground subsidence. In the methods of the presentdisclosure, only ground uplift was considered because carbon dioxideinjection causes pore pressure buildup in the reservoir and thus causesground uplift.

In order to see the effect of reservoir size selection on the grounduplift during carbon dioxide injection using a single injection well,carbon dioxide was injected for ten years, using both the small andlarge reservoir models. The ground uplift is shown in FIG. 41A-FIG. 41C(small model) and FIG. 42A-FIG. 42C (large model). The ground uplift isappreciably greater for the small model as compared to the large model,for the same injection parameters and injection period. The grounduplift attains its maximum value just above the injection point andextends for several kilometers around the injection point. As shown inFIG. 41A-FIG. 41C and FIG. 42A-FIG. 42C, the magnitude of the grounduplift increases with the injection of carbon dioxide into thereservoir.

FIG. 43 (small model) and FIG. 44 (large model) display the variation inthe values of the ground uplift during ten years of injection at variousinjection pressures. The ground uplift increases steadily as carbondioxide is injected into the reservoir, and its magnitude increases asthe injection pressure increases. The injection of carbon dioxide forlong time period at high injection pressure can cause high magnitude ofground uplift above the injection point. The ground uplift will extendfor several kilometers and will affect the people in the vicinity of theinjection reservoir.

Table 10 summarizes the ground uplift for the small and large models forthe 3, 6 and 10 year periods shown in FIG. 41A-FIG. 41C (small model),FIG. 42A-FIG. 42C (large model), FIG. 43 (small model) and FIG. 44(large model).

TABLE 10 Ground uplift with respect to model size at different timeperiods. Ground Uplift (mm) 4.1 years Reservoir 3 (1500 days) 6 10 Sizeyears (approximate) years years Small 11.6 17.5 19.1 26.8 Large 7.77 9.710.7 14.5

Carbon dioxide is normally injected using multiple injection wells. Inthe case of multiple injection wells, the pore pressure buildup is evenmore due to the reason that the pressure fronts from the two (or more)injection wells will interact and will exponentially increase themagnitude of the pore pressure and the ground uplift. In this case,ground uplift was calculated during carbon dioxide injection intoreservoir using multiple injection wells. FIG. 45A-FIG. 45D show that,as the size of the reservoir is increased during the geo-mechanicalmodeling of the reservoir, the magnitude of the ground uplift decreases.FIGS. 45A-45D illustrate the ground uplift (in mm) during carbon dioxideinjection into different size models: FIG. 45A in a reservoir of size2800×1800 meters, FIG. 45B in a reservoir of size 3000×2000 meters, FIG.45C in a reservoir of size 6000×4000 meters and FIG. 45D in a reservoirof size 9000×6000 meters. The magnitude of the ground uplift is found tobe higher in the case of carbon dioxide injection using multipleinjection wells than that for the case of the single injection well asexpected, as using multiple wells should result in higher volumes ofsequestered CO₂.

Table 11 summarizes the effect of reservoir size on ground uplift formultiple injection wells.

TABLE 11 Ground uplift with respect to reservoir size in multipleinjection wells. Reservoir 2800 × 3000 × 6000 × 9000 × Size 1800 20004000 6000 Ground 27.7 24.4 17.9 16.3 Uplift 7.77 9.7 10.7 14.5 (mm)

The reservoir is normally bound from all the sides with accompanyinggeological layers except the top surface of the reservoir that may bedeformed during carbon dioxide injection process. The reservoir cannotdeform freely horizontally due to the geological layers at the sides ofthe reservoir, however, if the permeability of the geologicalside-layers is high, then carbon dioxide may flow across the reservoirboundaries and penetrate into the side geological layers. The openboundary conditions will prevent the excessive pore pressure buildupduring carbon dioxide injection, thus resulting in relatively lessvalues of ground uplift in this case. FIG. 46A (closed boundary) andFIG. 46B (open boundary) show the effect of the boundary conditions onthe ground uplift. The magnitude of the ground uplift in case of theopen boundary conditions is less than that of the no-flow boundaryconditions. FIG. 46A shows a ground uplift of about 13.5 mm for theclosed boundary and FIG. 46B shows a ground uplift of about 7.5 mm forthe open boundary. A no-flow boundary condition can occur geologicallyif the reservoir block is bounded from all sides by impermeable faults.In this case, the flow of the injected carbon dioxide will be restrictedby the impermeable faults and thus the accumulation of the injectedcarbon dioxide will cause a high magnitude of pore pressure inside thereservoir and hence a high magnitude of ground uplift.

In order to see the effect of the reservoir size on the faultreactivation, carbon dioxide was injected at a depth of 1400 meters atan injection pressure of 26 MPa into the Biyadh reservoir (114, FIG. 1).Carbon dioxide was injected at a distance of 200 meters from a fault.FIG. 47A-47D illustrate the carbon dioxide saturation in the reservoirand overburden layers after carbon dioxide injection: FIG. 47A for asmall model after 5 years, FIG. 47B for a small model after 10 years,FIG. 47C for a large model after 5 years and 47D for a large model after10 years. The injection of carbon dioxide for ten years into thereservoir causes fault reactivation for both the small and large sizereservoirs. Comparison of FIG. 47B with FIG. 47D illustrates that thesaturation of carbon dioxide is greater in the overburden layers for thesmall size reservoir than for a large size reservoir after ten years ofcarbon dioxide injection. This leakage of a large quantity of carbondioxide in the small size reservoir indicates an increase in the faultpermeability, i.e. the fault reactivates or opens. FIG. 47A-FIG. 47Balso show that the fault is reactivated earlier at in the case of carbondioxide injection into the small size reservoirs at about 1700 days thaninto the large size reservoirs of FIG. 47C-FIG. 47D at about 4500 days.As shown in FIG. 48A and FIG. 48B, the magnitude of the pore pressure inthe Wasia overburden layer is greater in the case of a small sizereservoir (FIG. 48A) than in the large size reservoir (FIG. 48B). Thehigh magnitude of the pore pressure in the Wasia overburden layer forthe small size reservoir is due to the leakage of the large quantity ofhighly pressurized carbon dioxide.

A coupled stability analysis was performed for the Biyadh sandstonereservoir for both the small and large model sizes. For the stabilityanalysis of the reservoir, the Mohr-Coulomb failure criterion wasutilized to find the final stressed condition of the reservoir aftercarbon dioxide injection. The vertical stress due to the overburdenlayers was considered to be constant, while the changes in thehorizontal stresses due to the pore pressure variation during carbondioxide injection were allowed to vary. The pore pressure valuecorresponding to the maximum injection pressure was used for thestability analysis of the reservoir for both cases of small and largemodels. As shown in FIG. 48, the stressed conditions of the reservoirbefore carbon dioxide injection are shown by the dashed circle for boththe small and large models, which were based on the initial values ofreservoir stresses and pore pressure. As carbon dioxide was injectedinto the small and large reservoirs, the pore pressure increased, andeventually caused a change in the magnitude of the horizontal stressesin the reservoirs. The final stressed conditions for the small and largesize models are shown by the solid circles which demonstrate that thestability is highly dependent on the size of the reservoir that isselected for the modeling procedure. The smaller the size of thereservoir model, the greater the pressure buildup that will move thereservoir closer to the failure condition, as compared to the largermodel size.

The present disclosure describes methods for relating the rate ofinjection of CO₂ into a reservoir layer to pore pressure and effectivestresses in fractured and non-fractured layers. The pore pressure andeffective stresses are used to predict subsequent uplift of the caprock,leakage into the subsurface layers and long term stability of thereservoir.

Further, the above methods determine the effect on reducing the porepressure build-up and increasing the reservoir storage capacity byvarying both the number and arrangement of carbon dioxide injectionwells.

Additionally, the present disclosure describes methods for determiningthe effects of reservoir model size and different boundary conditions onpore pressure buildup, ground uplift, fault reactivation, and stabilityof the reservoir by means of the geo-mechanical modeling of thereservoir. Further determined are the number and placement of injectionwells and the relationship to pore pressure buildup, ground uplift,fault reactivation, and stability of the reservoir.

In summary:

i. For non-fractured caprock, carbon dioxide is restricted by thecaprock to spread only within the reservoir, whereas for fracturedcaprock, carbon dioxide leaks into the overburden layers, asanticipated. Accordingly, the pressure buildup attains higher values innon-fractured caprock. On the other hand, for fractured caprock, theleakage of carbon dioxide tends to increase the local pore pressure ofthe overburden layers. The location of the fracture zone in the caprockwas found to have an influence on the pore pressure in the overburdenlayers. It was observed that the pore pressure becomes higher as thefractured zone gets closer to the injection well. Excessive increase inpore pressure may cause leakage of carbon dioxide to the potable waterlayers and atmosphere. Therefore, CO₂ injection must be confined toinjecting a safe quantity of carbon dioxide into reservoirs that do notinclude active geological faults and fractures.

ii. The injection of carbon dioxide causes a considerable increase inthe pore pressure and the resulting ground uplift. For the case of thenon-fractured caprock, the ground uplift reaches its highest value justabove the injection point at the center of the reservoir. However, forthe case of the fractured caprock, the ground uplift is centered abovethe fractured zone. It is important to note that the increase in theground uplift just above the fractured zone can be instrumental in theidentification and localization of the fractured zone in the caprock.Further, the location of the fracture zone in the caprock alsoinfluences the magnitude of the vertical ground displacement in that themagnitude of the ground uplift is higher as the fracture zone getscloser to the injection well. The induced ground uplift due to injectionextends for several kilometers around the injection point.

iii. The permeability of the fractured zone has a significant influenceon the amount of carbon dioxide leakage into the overburden layers, andhence on the vertical ground uplift. It was observed that the verticalground displacement above the fractured zone decreases as thepermeability of the fractured zone decreases. The Mohr-Coulomb failurecriterion was used to perform the coupled stability analysis of thereservoir during injection. Because of carbon dioxide leakage into theoverburden layers in the case of fractured caprock, the pressure buildupin the reservoir did not attain enough high values to cause failure ofthe reservoir structure. Even for higher values of pressure buildup, inthe case of non-fractured caprock, the reservoir was found to maintainstability and remained on the safe side for the 10-year period of carbondioxide injection. The injection period, together with the safe valuesof the injection parameters, such as flow rate and injection pressure,must be calculated before carbon dioxide injection to ensure that thestored gas does not leak into the atmosphere and that the climate changemitigation strategies are not be jeopardized. The estimated safe valuesof the injection parameters may be considered as benchmark data forperforming similar carbon dioxide sequestration scenarios in reservoirs.

iv. Among various climate mitigation strategies, which may includerenewable energy sources, retrofitting buildings to become moreenergy-efficient, and developing more sustainable support systems, thecarbon capture and sequestration has great potential. The results of thepresent disclosure are demonstrated by a non-limiting example of amitigation strategy exploring the potential of one of the largestsandstone reservoirs in Saudi Arabia for carbon dioxide storage. TheBiyadh reservoir stretches over 250 km in length and 30 km in width,which is estimated to possess a storage capacity of 8 to 20 gigatons.Although the methods of the present disclosure have been described usinga specific carbon dioxide injection scenario in a Saudi Arabianreservoir, the geo-mechanical modeling, stability analysis, and modelingof leakage are broadly applicable to other geological sites worldwide.

v. Increasing the number of injection wells causes an increase in thepore pressure which significantly decreases the effective stresses onthe reservoir and drives the reservoir to move towards the failure line.Arranging injection wells in different patterns also affects the porepressure and hence the stability of the reservoir. For multipleinjection wells, if the injection wells are closer to each other, thepore pressure will significantly increase during carbon dioxideinjection. For the various injection scenarios, the reservoir remainedin a safe, stable condition. Four-injection well scenarios came closerto the failure line (of the Mohr-Coulomb failure envelope) as comparedto the other injection scenarios.

vi. When increasing the number of injection wells in the system, themaximum occupancy of CO₂ must be monitored in order not to exceed thecritical occupancy for the reservoir. The maximum occupancy wascalculated for different numbers of injection wells. For the case of theboosted injection using four wells, the occupancy was found to be 1.64%of the available pore volume of the reservoir, which is less than theallowable 3% limit for the closed reservoir condition.

vii. Ground vertical uplift was noted to increase appreciably with anincrease in the number of injection wells. Although the use of fourinjection wells did not exceed the maximum occupancy limit, it caused asignificant reduction in the effective stresses in the reservoir.Consequently, the reservoir was driven towards the failure line, inaddition to reaching higher values of ground uplift that extended forseveral kilometers surrounding the injection wells.

viii. One of the key factors for deciding the optimum number ofinjection wells and the optimum well arrangement is the accumulation ofcarbon dioxide during injection. The results of the numericalinvestigation demonstrate it is advisable to avoid placing the injectionwells very close to each other or very close to the boundaries of thereservoir.

ix. For multi-well injection scenarios, the above results can easilysuggest the best possible well arrangement. For instance, it was shownthat two wells spaced at some optimum distance would achieve maximumreservoir stability, maximum reservoir storage capacity and lower valuesof the vertical ground uplift. For the three-well and four-wellarrangements, although the storage capacity could reach higher values,this benefit is compromised by comparatively less reservoir stabilityand higher values of ground vertical uplift.

x. The pore pressure buildup in the case of the large reservoir modelwas found to be lower as compared to the small model due to the factthat in large model the closed boundaries of the reservoir are far awayfrom the injection well and this facilitates the rapid flow of carbondioxide along the reservoir. In the small model of the reservoir, theclosed boundaries restrict the flow of carbon dioxide and thus the rateof pore pressure buildup increases. Furthermore, the pore pressureincreases as the value of the carbon dioxide injection pressure isincreased. Similarly in the case of multiple injection wells, themagnitude of the pore pressure decreases as the size of the reservoir isincreased. It was concluded that the selection of a representativereservoir volume with a size different from that of the actual reservoirinfluenced the estimated pore pressure buildup due to carbon dioxideinjection. Moreover, for the open boundary condition, the magnitude ofpore pressure after carbon dioxide injection was found to be relativelylower compared to the no-flow boundary condition.

xi. The ground uplift was found to be higher for the small sizereservoir model as compared to the large reservoir model for the sameinjection parameters and injection period. The ground uplift has amaximum value at the location just above the injection point, yet itextended for several kilometers around the injection point. Themagnitude of the ground uplift is higher in the case of carbon dioxideinjection using multiple injection wells as compared to the CO₂injection using single injection well. The value of the ground upliftwas found to be lower in the case of an open boundary condition. TheMohr-Coulomb failure criterion demonstrated that the stability analysisis highly dependent on the size of the reservoir used in the modelingprocedure. It was also observed that the smaller the size of thereservoir, the larger the pressure buildup, and the final stresscondition of the reservoir was closer to the failure envelope comparedto the larger size reservoir model.

xii. An existing fault was shown to be reactivated earlier in the caseof small size reservoir as compared to case of large size reservoir, andwas shown to be followed by a higher saturation of carbon dioxide in theoverburden layers. The leakage of a large quantity of carbon dioxide inthe case of small size reservoir is an indication of the increase in thefault permeability. The magnitude of the pore pressure in the overburdenlayers was shown to be relatively higher in the case of small sizereservoir due to the leakage of the large quantity highly pressurizedcarbon dioxide.

Additionally, the methods of the present disclosure provide thefollowing benefits:

The method may calculate the dimensions of the fracture and identify thelocation of the fracture from the measured magnitude of the grounduplift during fluid injection into the reservoir. If the location of thefracture or fault is known, the resulting ground uplift can also becalculated using this technique during the fluid injection process. Ifthe permeability of the fracture or fault is known, the resulting grounduplift can be calculated using this technique.

The methods may provide an alarming system for the newly initiatedfractures, as well as the reactivation of the already existing fracturesand faults, by continuously monitoring the ground uplift. The initiationof new fractures and the re-activation of the already existing fracturesand faults will tend to change the ground uplift pattern which will helpto identify the leakage point.

The methods may identify the saturation of the leaked fluid (CO₂ etc.)in the overburden layers after the activation of the fracture or faultin the caprock.

The methods may identify the magnitude of the pore pressure buildup inthe overburden layers after the leakage of the injected fluid from thereservoir.

The methods may relate the pore pressure buildup in the overburdenlayers with the dimensions of the fracture or fault after the fluidleakage to the overburden layers.

The methods may relate the pore pressure buildup in the overburdenlayers with the location of the fracture or fault after the fluidleakage to the overburden layers.

The methods may perform the post injection monitoring of the grounduplift and can identify any potential fluid leakage from the reservoirand provide a leakage alarm.

The methods may be used to perform post injection monitoring of the porepressure in the overburden layers and identify any potential fluidleakage from the reservoir and provide a leakage alarm.

The alarm may be an one of an audible alarm, a visual display indicatoron a monitoring computer, a flashing light, an email, a text message, anautomatic telephone call, and the like.

The sedimentary reservoirs that contain water in the rock matrix providea more secure CO2 sequestration medium. The injection of carbon dioxidecauses a huge increase in the reservoir pore pressure and provokes thesubsequent ground uplift. An excessive increase in pore pressure mayalso cause leakage of carbon dioxide into the potable water layers andto the atmosphere, thus leading to severe global climatic changes. Inorder to maintain the integrity of the sequestration process, it iscrucial to inject a safe quantity of carbon dioxide into thesequestration site. Accordingly, the injection period and the safevalues of injection parameters, like flow rate and injection pressure,need to be calculated a priori to ensure that the stored carbon dioxidewill not leak into the atmosphere and jeopardize a climate mitigationstrategy. To model carbon dioxide injection in reservoirs having a basefluid, such as water, one has to perform a two-phase flow modeling forboth the injected and base fluids. In the present disclosure, asimulation of carbon dioxide being injected into Biyadh reservoir isperformed, wherein the two-phase flow through the reservoir structure istaken into account. This investigation aims to estimate the safeparameter values for carbon dioxide injection into the Biyadh reservoir,in order to avoid leakage of carbon dioxide through the caprock. In thiscontext, the two cases of a fractured and non-fractured caprock areconsidered. To ensure a safe sequestration mechanism, the coupledreservoir stability analysis is performed to estimate the safe values ofthe injection parameters, thus furnishing data for a reliable globalclimate change mitigation strategy. The obtained results demonstratedthat the injection of carbon dioxide has caused a maximum pore pressureincrease of 25 MPa and a ground uplift of 35 mm.

The injection of CO2 into the reservoir, during long-term subsurfacecontainment of CO2, increases the pore pressure, as well as theadsorption induced strains. The associated decrease in permeabilitycauses the transport of the injected CO2 to decrease to a criticalvalue, after which it becomes impossible to transport the injectedcarbon dioxide to regions of the reservoir far away from the injectionwell, regardless of its capacity. This problem initiated the need formultiple injection wells. The present investigation considers a dualporous carbonate reservoir. A new methodology is developed for reducingthe pore pressure build-up and increasing the reservoir storage capacityby varying both the number and arrangement of the carbon dioxideinjection wells. An equation-based finite element method is utilized forthe numerical modelling of various carbon dioxide injection scenariosfor Ghawar Arab-D carbonate reservoir. The obtained results demonstratedthe significance of changing the number and arrangement of the injectionwells and suggested the existence of an optimum arrangement.

One of the effective global mitigation strategies is sequestration ofhuge quantity of carbon dioxide deep below the ground level for a longperiod of time. During the carbon dioxide injection process, thereservoir pressure and deformation responses will be different fordifferent reservoir's size and boundary conditions. In thisinvestigation, the effects of reservoir size and boundary conditions areinvestigated by means of geo-mechanical modeling of the deep Biyadhsandstone reservoir in Saudi Arabia. Currently carbon dioxide is notinjected into the actual Biyadh reservoir. In this investigativemodeling, carbon dioxide was injected for an injection period of tenyears using a single injection well at the center of the reservoir. Thedeveloped modeling scheme for a single injection well has been extendedfurther to include multiple injection wells. For multiple injectionwells, the reservoir size and locations of injection wells were variedto evaluate their effect on the pore pressure buildup and ground uplift.The reservoir stability analysis was performed using Mohr-Coulombfailure criterion for both small and large reservoir models, with thesame injection parameters. The simulation results demonstrated thatpressure buildup and ground uplift are relatively higher for reservoirswith small sizes and closed boundaries, while in the case of large sizesand open boundaries, the pore pressure buildup and ground uplift arerelatively lower. Injecting carbon dioxide with multiple injection wellswill cause pore pressure buildup of huge magnitudes. Moreover, theeffect of the reservoir size and boundary conditions on the reactivationof faults during carbon dioxide injection has been evaluated. Thestability analysis performed in this study shows that injecting carbondioxide into larger size reservoir is safer as compared to smaller sizereservoir.

Next, details of the hardware description of the computing environmentused to run the COMSOL, CMG-GEM, MATLAB programs and utilize theBarton-Bandis model to relate changes in effective stresses to caprockfracture permeability, utilize the Mohr-Coulomb criterion to predict thestability of the reservoir, utilize the Warren and Root fracture modelto predict fracture reactivation and to do the calculations according toexemplary embodiments is described with reference to FIG. 50. In FIG.50, a controller 5000 is a computing device which includes a CPU 5001which performs the processes described above/below. The process data andinstructions may be stored in memory 5002. These processes andinstructions may also be stored on a storage medium disk 5004 such as ahard drive (HDD) or portable storage medium or may be stored remotely.

Further, the claimed advancements are not limited by the form of thecomputer-readable media on which the instructions of the inventiveprocess are stored. For example, the instructions may be stored on CDs,DVDs, in FLASH memory, RAM, ROM, PROM, EPROM, EEPROM, hard disk or anyother information processing device with which the computing devicecommunicates, such as a server or computer.

Further, the claimed advancements may be provided as a utilityapplication, background daemon, or component of an operating system, orcombination thereof, executing in conjunction with CPU 5001 and anoperating system such as Microsoft Windows 7, UNIX, Solaris, LINUX,Apple MAC-OS and other systems known to those skilled in the art.

The hardware elements in order to achieve the computing device may berealized by various circuitry elements, known to those skilled in theart. For example, CPU 5001 may be a Xenon or Core processor from Intelof America or an Opteron processor from AMD of America, or may be otherprocessor types that would be recognized by one of ordinary skill in theart. Alternatively, the CPU 5001 may be implemented on an FPGA, ASIC,PLD or using discrete logic circuits, as one of ordinary skill in theart would recognize. Further, CPU 5001 may be implemented as multipleprocessors cooperatively working in parallel to perform the instructionsof the inventive processes described above.

The computing device in FIG. 50 also includes a network controller 5006,such as an Intel Ethernet PRO network interface card from IntelCorporation of America, for interfacing with network 5060. As can beappreciated, the network 5060 can be a public network, such as the

Internet, or a private network such as an LAN or WAN network, or anycombination thereof and can also include PSTN or ISDN sub-networks. Thenetwork 5060 can also be wired, such as an Ethernet network, or can bewireless such as a cellular network including EDGE, 3G and 4G wirelesscellular systems. The wireless network can also be WiFi, Bluetooth, orany other wireless form of communication that is known.

The computing device further includes a display controller 5008, such asa NVIDIA GeForce GTX or Quadro graphics adaptor from NVIDIA Corporationof America for interfacing with display 5010, such as a Hewlett PackardHPL2445w LCD monitor. A general purpose I/O interface 5012 interfaceswith a keyboard and/or mouse 5014 as well as a touch screen panel 5016on or separate from display 5010. General purpose I/O interface alsoconnects to a variety of peripherals 5018 including printers andscanners, such as an OfficeJet or DeskJet from Hewlett Packard.

A sound controller 5020 is also provided in the computing device such asSound Blaster X-Fi Titanium from Creative, to interface withspeakers/microphone 5022 thereby providing sounds and/or music.

The general purpose storage controller 5024 connects the storage mediumdisk 5004 with communication bus 5026, which may be an ISA, EISA, VESA,PCI, or similar, for interconnecting all of the components of thecomputing device. A description of the general features andfunctionality of the display 5010, keyboard and/or mouse 5014, as wellas the display controller 5008, storage controller 5024, networkcontroller 5006, sound controller 5020, and general purpose I/Ointerface 5012 is omitted herein for brevity as these features areknown.

The exemplary circuit elements described in the context of the presentdisclosure may be replaced with other elements and structureddifferently than the examples provided herein. Moreover, circuitryconfigured to perform features described herein may be implemented inmultiple circuit units (e.g., chips), or the features may be combined incircuitry on a single chipset, as shown on FIG. 51.

FIG. 51 shows a schematic diagram of a data processing system, accordingto certain embodiments, for performing the functions of the exemplaryembodiments. The data processing system is an example of a computer inwhich code or instructions implementing the processes of theillustrative embodiments may be located.

In FIG. 51, data processing system 5100 employs a hub architectureincluding a north bridge and memory controller hub (NB/MCH) 5125 and asouth bridge and input/output (I/O) controller hub (SB/ICH) 5120. Thecentral processing unit (CPU) 5130 is connected to NB/MCH 5125. TheNB/MCH 5125 also connects to the memory 5145 via a memory bus, andconnects to the graphics processor 5150 via an accelerated graphics port(AGP). The NB/MCH 5125 also connects to the SB/ICH 5120 via an internalbus (e.g., a unified media interface or a direct media interface). TheCPU Processing unit 5130 may contain one or more processors and even maybe implemented using one or more heterogeneous processor systems.

For example, FIG. 52 shows one implementation of CPU 5130. In oneimplementation, the instruction register 5238 retrieves instructionsfrom the fast memory 5240. At least part of these instructions arefetched from the instruction register 5238 by the control logic 5236 andinterpreted according to the instruction set architecture of the CPU5130. Part of the instructions can also be directed to the register5232. In one implementation the instructions are decoded according to ahardwired method, and in another implementation the instructions aredecoded according a microprogram that translates instructions into setsof CPU configuration signals that are applied sequentially over multipleclock pulses. After fetching and decoding the instructions, theinstructions are executed using the arithmetic logic unit (ALU) 5234that loads values from the register 5232 and performs logical andmathematical operations on the loaded values according to theinstructions. The results from these operations can be feedback into theregister and/or stored in the fast memory 5240. According to certainimplementations, the instruction set architecture of the CPU 5130 canuse a reduced instruction set architecture, a complex instruction setarchitecture, a vector processor architecture, a very large instructionword architecture. Furthermore, the CPU 5130 can be based on the VonNeuman model or the Harvard model. The CPU 5130 can be a digital signalprocessor, an FPGA, an ASIC, a PLA, a PLD, or a CPLD. Further, the CPU5130 can be an x86 processor by Intel or by AMD; an ARM processor, aPower architecture processor by, e.g., IBM; a SPARC architectureprocessor by Sun Microsystems or by Oracle; or other known CPUarchitecture.

Referring again to FIG. 51, the data processing system 5100 can includethat the SB/ICH 5120 is coupled through a system bus to an I/O Bus, aread only memory (ROM) 5156, universal serial bus (USB) port 5164, aflash binary input/output system (BIOS) 51651, and a graphics controller51551. PCI/PCIe devices can also be coupled to SB/ICH 515151 through aPCI bus 5162.

The PCI devices may include, for example, Ethernet adapters, add-incards, and PC cards for notebook computers. The Hard disk drive 5160 andCD-ROM 5166 can use, for example, an integrated drive electronics (IDE)or serial advanced technology attachment (SATA) interface. In oneimplementation the I/O bus can include a super I/O (SIO) device.

Further, the hard disk drive (HDD) 5160 and optical drive 5166 can alsobe coupled to the SB/ICH 5120 through a system bus. In oneimplementation, a keyboard 5170, a mouse 5172, a parallel port 5178, anda serial port 5176 can be connected to the system bus through the I/Obus. Other peripherals and devices that can be connected to the SB/ICH820 using a mass storage controller such as SATA or PATA , an Ethernetport, an ISA bus, a LPC bridge, SMBus, a DMA controller, and an AudioCodec.

Moreover, the present disclosure is not limited to the specific circuitelements described herein, nor is the present disclosure limited to thespecific sizing and classification of these elements. For example, theskilled artisan will appreciate that the circuitry described herein maybe adapted based on changes on battery sizing and chemistry, or based onthe requirements of the intended back-up load to be powered.

The functions and features described herein may also be executed byvarious distributed components of a system. For example, one or moreprocessors may execute these system functions, wherein the processorsare distributed across multiple components communicating in a network.The distributed components may include one or more client and servermachines, which may share processing, as shown by FIG. 53, in additionto various human interface and communication devices (e.g., displaymonitors, smart phones, tablets, personal digital assistants (PDAs)).The network may be a private network, such as a LAN or WAN, or may be apublic network, such as the Internet. Input to the system may bereceived via direct user input and received remotely either in real-timeor as a batch process. Additionally, some implementations may beperformed on modules or hardware not identical to those described.Accordingly, other implementations are within the scope that may beclaimed.

The above-described hardware description is a non-limiting example ofcorresponding structure for performing the functionality describedherein.

Obviously, numerous modifications and variations of the presentdisclosure are possible in light of the above teachings. It is thereforeto be understood that within the scope of the appended claims, theinvention may be practiced otherwise than as specifically describedherein.

The invention claimed is:
 1. A method for carbon dioxide sequestrationin a geologic reservoir having a caprock and a plurality of subsurfacelayers between the geologic reservoir and the caprock, comprising:constructing a reservoir model, by a computer having programinstructions, a display and a reservoir database stored therein, thatwhen executed by one or more processors of the computer, causes the oneor more processors to construct the reservoir model which includes:reservoir boundary conditions, a three dimensional size of the geologicreservoir, faults in the geologic reservoir, lithography, rockdensities, porosities, and depths of the caprock and the plurality ofsubsurface layers; initial values of horizontal stresses (σ), volumetricstrain (ε_(v)), pore pressure of water (P_(water)), pore pressure ofcarbon dioxide (P_(carbon dioxide)), permeabilities (k₀), pressure wavevelocities and shear wave velocities of the geologic reservoir, thecaprock and the subsurface layers; a plurality of injection wellslocated in an array formation in the geologic reservoir, each injectionwell supplying carbon dioxide at a supercritical injection pressure intoat least one subsurface layer; predicting, by the computer, changes inthe porosity, the horizontal stresses, the pore pressures, thepermeabilities, the pressure wave velocities and the shear wavevelocities based on each supercritical_injection pressure; calculating,by the computer, changes in a multiphase flow rate of carbon dioxide andwater at each injection site at intervals over a selected period oftime, wherein the period of time is selected from the range of one yearto one hundred years; updating, by the computer, each supercriticalinjection pressure at each interval based on the changes in themultiphase flow rate at each injection well; wherein a flow rate ofwater, Q_(water), at each injection site is given by:${Q_{water} = {{\frac{\partial}{\partial t}\left( {\rho_{water}\varnothing^{*}S_{water}} \right)} - {\nabla{\cdot \left( {\rho_{water}v_{water}} \right)}}}},$where ρ_(water) is a density of water, Ø* is an updated porosity of thereservoir, given by Ø*=(1−ε_(v)), where Ø is an initial porosity of thereservoir, ε_(v) is the volumetric strain in the reservoir, S_(water) isa saturation of the water, -V_(water) is a flow of the water percross-sectional unit area; wherein a flow rate of carbon dioxide,Q_(carbon dioxide), at each injection site is given by:${Q_{{carbon}\mspace{14mu}{dioxide}} = {{\frac{\partial}{\partial t}\left( {\rho_{{carbon}\mspace{14mu}{dioxide}}\varnothing^{*}S_{{carbon}\mspace{14mu}{dioxide}}} \right)} - {\nabla{\cdot \left( {\rho_{{carbon}\mspace{14mu}{dioxide}}v_{{carbon}\mspace{14mu}{dioxide}}} \right)}}}},$where ρ_(carbon dioxide) is a density of the carbon dioxide,S_(carbon dioxide) is a saturation of the carbon dioxide,ν_(carbon dioxide) is a flow of the carbon dioxide per cross-sectionalunit area; wherein coupling between the saturation of the carbon dioxideand the saturation of water is given by:S _(water) +S _(carbon dioxide)=1; wherein coupling between the porepressure of the carbon dioxide, P_(carbon dioxide), and the porepressure of water, P_(water) is given by:P _(carbon dioxide)(S _(water))=P _(carbon dioxide) −P _(water);receiving, by the computer, a series of satellite surface imagesincluding topology images of the geologic reservoir over the period oftime; determining, by the computer, an amount of caprock uplift and alocation of the caprock uplift based on changes in the topology imagesof the geologic reservoir at each interval of the period of time;determining, by the computer, each volume of carbon dioxide sequesteredin the geologic_reservoir at each updated supercritical injectionpressure at each interval of the period of time; correlating, by thecomputer, the updated supercritical injection pressure at each injectionwell at each interval of the period of time to the amount of caprockuplift over each injection well, and the volume of carbon dioxidesequestered in the geologic reservoir; minimizing the caprock uplift andmaximizing the volume of carbon dioxide sequestered by adjusting thenumber of injection wells, the array formation and the updatedsupercritical injection pressure at each injection well; and rendering,on the display, a representation of the geologic reservoir displayingthe number of injection wells, the array formation, the locations ofcaprock uplift and the updated injection pressures at each injectionwell which achieve the minimized caprock uplift and the maximized volumeof carbon dioxide sequestered; monitoring, by the computer, the caprockuplift over each injection well over each interval of the selectedperiod of time; when the caprock uplift over a particular injection wellexceeds a threshold selected from the range of 0 mm to 25 mm,identifying carbon dioxide leakage from the particular injection well,and transmitting, by the computer, an alarm to the particular injectionwell to lower the updated supercritical injection pressure.
 2. Themethod of claim 1, wherein the geologic reservoir is a carbonatereservoir including porous rocks, wherein the porous rocks include atleast one of grainstone, packstone, wackestone, mudstone, bafflestone,bindstone, framestone, floatstone, rudstone and shale, wherein themultiphase flow rate is lowered due to absorption of carbon dioxide intothe porous rocks.
 3. The method of claim 1, further comprising:identifying, by the computer, the geologic reservoir as a sandstonereservoir including saline water; calculating, by the computer, changesin the multiphase flow rate as the injected carbon dioxide dissolves inthe saline water, wherein the changes in the multiphase flow rate resultfrom an increased ratio of carbon dioxide to water.
 4. The method ofclaim 1, wherein determining changes in the porosity is based on Ø*=Ø(1−ε_(v)), where Ø is the porosity and Ø* is the changed porosity.
 5. Themethod of claim 1, further comprising: wherein the program instructionsinclude a Mohr-Coulomb failure criterion; and calculating, by thecomputer, the Mohr-Coulomb failure criterion to determine a stability ofthe geologic reservoir based on the changes in pore pressures,horizontal stresses and volumetric strains.
 6. The method of claim 5,further comprising predicting safe values of the updated supercriticalinjection pressures based on the Mohr-Coulomb failure criterion.
 7. Themethod of claim 1, further comprising: wherein the program instructionsinclude a Barton-Bandis model; determining, by the computer, changes inthe permeability of the caprock based on the Barton-Bandis model; andidentifying a fracture in the caprock based on a rise in thepermeability of the caprock.
 8. The method of claim 1, furthercomprising: wherein the program instructions include a Warren and Rootfracture model; determining, by the computer, changes in thepermeability of at least one fault based on the Warren and Root fracturemodel; and identifying a reactivation of at the least one fault.
 9. Themethod of claim 8, further comprising calculating carbon dioxidesaturation in the subsurface layers based on the changes in thepermeability of the least one fault; determining a fault location andfault dimensions of the least one fault; and predicting the amount ofcaprock uplift due to the carbon dioxide saturation.
 10. The method ofclaim 1, wherein the reservoir boundary conditions are at least one ofan open boundary and a closed boundary.
 11. The method of claim 1,further comprising configuring the number and array formation of thearray of injection wells based on the three dimensional size of thegeologic reservoir and the boundary conditions.
 12. The method of claim1, wherein the program instructions further include geo-mechanicalmodelling instructions; and wherein the geo-mechanical modellingincorporates the initial values of geologic reservoir density, pressurewave velocity and shear wave velocity to calculate changes in themodulus of elasticity, the shear modulus, and a bulk modulus due to thechanges in the supercritical injection pressures.
 13. The method ofclaim 1, further comprising performing post injection monitoring afterthe period of time, of the pore pressure in the subsurface layers;identifying carbon dioxide leakage from the geologic reservoir based ondecreased levels of the pore pressures; and displaying, on the display,a leakage alert.
 14. The method of claim 1, further comprising:adjusting, by the computer, the array of injection wells to minimize thecaprock uplift and maximize the volume of carbon dioxide sequestered bytransmitting a command to each injection well in the array of injectionwells to perform one of: starting to inject carbon dioxide at thesupercritical injection pressure, continuing to inject carbon dioxide atthe supercritical injection pressure, ceasing the injection of carbondioxide, and changing the supercritical injection pressure to acommanded supercritical injection pressure.
 15. An alarming system forleakage in a geologic reservoir sequestering carbon dioxide, thegeologic reservoir having a caprock and a plurality of subsurface layersbetween the geologic reservoir and the caprock, comprising: a satellitesurface imaging database including a series of topology images of thegeologic reservoir taken over a selected period of time, wherein theperiod of time is selected from the range of one year to one hundredyears; a memory storing the satellite surface imaging database, areservoir database and program instructions; a computer comprising aprocessor with circuitry configured to cause the one or more processorsto perform the program instructions to construct a reservoir model whichincludes: reservoir boundary conditions, a three dimensional size of thegeologic reservoir, faults in the geologic reservoir, lithography, rockdensities, porosities, and depths of the caprock and the plurality ofsubsurface layers; initial values of horizontal stresses (σ), volumetricstrain, (ε_(v)), pore pressure of water (P_(water)), pore pressure ofcarbon dioxide (P_(carbon dioxide)), permeabilities, pressure wavevelocities and shear wave velocities of the geologic reservoir, thecaprock and the subsurface layers; a plurality of injection wellslocated in an array formation in the geologic reservoir, each injectionwell supplying carbon dioxide at a supercritical injection pressure intoat least one subsurface layer; wherein the computer is furtherconfigured to: predict changes in the porosity, the horizontal stresses,the pore pressures, the permeabilities, the pressure wave velocities andthe shear wave velocities of the geologic reservoir, the caprock and thesubsurface layers, based on each supercritical injection pressure;calculate changes in a multiphase flow rate of carbon dioxide and waterat each injection site at intervals over the selected period of time;update each supercritical injection pressure at each interval based onthe changes in the multiphase flow rate at each injection well; whereina flow rate of water, Q_(water,) at each injection site is given by:${Q_{water} = {{\frac{\partial}{\partial t}\left( {\rho_{water}\varnothing^{*}S_{water}} \right)} - {\nabla{\cdot \left( {\rho_{water}v_{water}} \right)}}}},$where ρ_(water) is a density of water, Ø* is an updated porosity of thereservoir, given by Ø* =Ø(1−ε_(ν)), where Ø is an initial porosity ofthe reservoir, ε_(ν)is the volumetric strain in the reservoir, S_(water)is a saturation of the water, ν_(water) is a flow of the water percross-sectional unit area; wherein a flow rate of carbon dioxide,Q_(carbon dioxide), at each injection site is given by:${Q_{{carbon}\mspace{14mu}{dioxide}} = {{\frac{\partial}{\partial t}\left( {\rho_{{carbon}\mspace{14mu}{dioxide}}\varnothing^{*}S_{{carbon}\mspace{14mu}{dioxide}}} \right)} - {\nabla{\cdot \left( {\rho_{{carbon}\mspace{14mu}{dioxide}}v_{{carbon}\mspace{14mu}{dioxide}}} \right)}}}},$where ρ_(carbon dioxide) is a density of the carbon dioxide,S_(carbon dioxide) is a saturation of the carbon dioxide,ν_(carbon dioxide) is a flow of the carbon dioxide per cross-sectionalunit area; wherein coupling between the saturation of the carbon dioxideand the saturation of water is given by:S _(water) +S _(carbon dioxide)=1; wherein coupling between the porepressure of the carbon dioxide, P_(carbon dioxide), and the porepressure of water, P_(water), is given by:P _(carbon dioxide)(S _(water))=P _(carbon dioxide) −P _(water);determine undetermine an amount of caprock uplift and a location of thecaprock uplift at each injection well based on comparing changes in thetopology images of the geologic reservoir at each interval of theselected period of time; compare the amount caprock uplift at eachinjection well at each interval to a threshold; identify carbon dioxideleakage from a particular injection well when the caprock uplift overthe particular injection well exceeds a threshold selected from therange of 0 mm to 25 mm; a display operatively connected to the computer;wherein the computer is further configured to: render, on the display, arepresentation of the geologic reservoir displaying the plurality ofinjection wells, the array formation, the locations of caprock upliftand the updated supercritical injection pressure at each injection well;display an alert on the display when the caprock uplift at theparticular injection well exceeds the threshold; and transmit an alarmto the particular injection well to lower the updated supercriticalinjection pressure.
 16. The alarming system of claim 15, wherein thecomputer is further configured to: determine a volume of carbon dioxidesequestered in the geologic reservoir at each updated supercriticalinjection pressure at each interval of the selected period of time;correlate the updated supercritical injection pressure at each injectionwell at each interval of the period of time to the amount of caprockuplift and the volume of carbon dioxide sequestered in the geologicreservoir; adjust the number of injection wells, the array formation andthe updated supercritical injection pressure at each injection well tominimize the caprock uplift and maximize the volume of carbon dioxidesequestered in the geologic reservoir.
 17. The alarming system of claim16, wherein the computer is further configured to: respond to the alarmby adjusting the number of injection wells, the array formation and thesupercritical injection pressure at each injection well to minimize thecaprock uplift and maximize the volume of carbon dioxide sequestered;and transmit a command to each injection well in the array of injectionwells to perform one of: start injecting carbon dioxide at thesupercritical injection pressure, continue to inject carbon dioxide atthe supercritical injection pressure, cease the injection of carbondioxide, and change the supercritical injection pressure to a commandedsupercritical injection pressure.
 18. A non-transitory computer readablemedium having instructions stored therein that, when executed by one ormore processors, cause the one or more processors to perform a methodfor monitoring the sequestration of carbon dioxide in a geologicreservoir having a caprock and a plurality of subsurface layers betweenthe geologic reservoir and the caprock, comprising: constructing areservoir model, from a reservoir database stored in the non-transitorycomputer readable medium, which includes: reservoir boundary conditions,a three dimensional size of the geologic reservoir, faults in thegeologic reservoir, lithography, rock densities, porosities, and depthsof the caprock and the plurality of subsurface layers; initial values ofhorizontal stresses (σ), volumetric strain (ε₈₄), pore pressures ofwater (P_(water)), pore pressures of carbon dioxide(P_(carbon dioxide)), permeabilities (k₀), pressure wave velocities andshear wave velocities of the geologic reservoir, the caprock and thesubsurface layers; a plurality of injection wells located in an arrayformation in the geologic reservoir, each injection well supplyingcarbon dioxide at a supercritical injection pressure into at least onesubsurface layer; predicting, by the computer, changes in the porosity,the horizontal stresses, the pore pressures, the permeabilities, thepressure wave velocities and the shear wave velocities based on eachsupercritical injection pressure; calculating, by the computer, changesin a multiphase flow rate of carbon dioxide and water at each injectionsite at intervals over a selected period of time, wherein the period oftime is selected from the range of one year to one hundred years;updating, by the computer, each supercritical injection pressure at eachinterval based on the changes in the multiphase flow rate at eachinjection well; wherein a flow rate of water, Q_(water,) at eachinjection site is given by:${Q_{water} = {{\frac{\partial}{\partial t}\left( {\rho_{water}\varnothing^{*}S_{water}} \right)} - {\nabla{\cdot \left( {\rho_{water}v_{water}} \right)}}}},$where ρ_(water) is a density of water, Ø* is an updated porosity of thereservoir, given by Ø*=Ø(1−ε_(v)), where Ø is an initial porosity of thereservoir, ε_(v) is the volumetric strain in the reservoir, S_(water) isa saturation of the water, ν_(water) a flow of the water percross-sectional is unit area; wherein a flow rate of carbon dioxide,Q_(carbon dioxide), at each injection site is given by:${Q_{{carbon}\mspace{14mu}{dioxide}} = {{\frac{\partial}{\partial t}\left( {\rho_{{carbon}\mspace{14mu}{dioxide}}\varnothing^{*}S_{{carbon}\mspace{14mu}{dioxide}}} \right)} - {\nabla{\cdot \left( {\rho_{{carbon}\mspace{14mu}{dioxide}}v_{{carbon}\mspace{14mu}{dioxide}}} \right)}}}},$where ρ_(carbon dioxide) is a density of the carbon dioxide,S_(carbon dioxide) is a saturation of the carbon dioxide,ν_(carbon dioxide) is a flow of the carbon dioxide per cross-sectionalunit area; wherein coupling between the saturation of the carbon dioxideand the saturation of water is given by:S _(water) +S _(carbon dioxide)=1; wherein coupling between the porepressure of the carbon dioxide, P_(carbon dioxide), and the porepressure of water, P_(water) is given by:P _(carbon dioxide)(S_(water))=P _(carbon dioxide) −P _(water);receiving, by the computer, a series of satellite surface imagesincluding topology images of the geologic reservoir over the period oftime; determining an amount of caprock uplift and a location of thecaprock uplift based on changes in the topology images of the geologicreservoir at each interval of the period of time; determining eachvolume of carbon dioxide sequestered in the geologic reservoir at eachupdated supercritical injection pressure at each interval of the periodof time; correlating the updated supercritical injection pressure ateach injection well at each interval of the period of time to the amountof caprock uplift over each injection well, and the volume of carbondioxide sequestered in the geologic reservoir; minimizing the caprockuplift and maximizing the volume of carbon dioxide sequestered byadjusting the number of injection wells, the array formation and theupdated supercritical injection pressure at each injection well; andrendering on the display, a representation of the geologic reservoirdisplaying the number of injection wells, the array formation, thelocations of caprock uplift and the updated injection pressures at eachinjection well which achieve the minimized caprock uplift and themaximized volume of carbon dioxide sequestered; monitoring the caprockuplift over each injection well over each interval of the selectedperiod of time; when the caprock uplift over a particular injection wellexceeds a threshold selected from the range of 0 mm to 25 mm,identifying carbon dioxide leakage from the particular injection well,and transmitting an alarm to the particular injection well to lower theupdated supercritical injection pressure.
 19. The non-transitorycomputer readable medium method of claim 18, wherein the programinstructions include a Mohr-Coulomb failure criterion; and calculating,by the computer, the Mohr-Coulomb failure criterion representing astability of the geologic reservoir based on the changes in porepressures, horizontal stresses and volumetric strains.
 20. Thenon-transitory computer readable medium method of claim 18, furthercomprising: adjusting the array of injection wells to minimize thecaprock uplift and maximize the volume of carbon dioxide sequestered bytransmitting a command to each injection well in the array of injectionwells to perform one of: starting to inject carbon dioxide at thesupercritical injection pressure, continuing to inject carbon dioxide atthe supercritical injection pressure, ceasing the injection of carbondioxide, and changing the supercritical injection pressure to acommanded supercritical injection pressure.